Journal articles: 'Disjunctive inference'

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Milne, Peter. "Disjunction and Disjunctive Syllogism." Canadian Journal of Philosophy 28, no. 1 (March 1998): 21–32. http://dx.doi.org/10.1080/00455091.1998.10715969.

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The validity of argument by disjunctive syllogism (henceforth, DS) has been denied by proponents of relevant and paraconsistent logic (who are sometimes one and the same). DS is stigmatised for its role in inferences — most notably C.I. Lewis's derivation of that fallacy of irrelevance ex falso quodlibet (EFQ) — that involve both it and other rules of inference governing disjunction, or, to speak more precisely, other rules of inference taken to apply to the very same disjunction that obeys DS. In avoiding these inferences the road less travelled is to deny the identity rather than to deny DS: what follows is, then, an exercise in disjoining disjunctions.

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Booth, Richard, and Ivan Varzinczak. "Conditional Inference under Disjunctive Rationality." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 7 (May 18, 2021): 6227–34. http://dx.doi.org/10.1609/aaai.v35i7.16774.

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The question of conditional inference, i.e., of which conditional sentences of the form ``if A then, normally, B'' should follow from a set KB of such sentences, has been one of the classic questions of AI, with several well-known solutions proposed. Perhaps the most notable is the rational closure construction of Lehmann and Magidor, under which the set of inferred conditionals forms a rational consequence relation, i.e., satisfies all the rules of preferential reasoning, *plus* Rational Monotonicity. However, this last named rule is not universally accepted, and other researchers have advocated working within the larger class of *disjunctive* consequence relations, which satisfy the weaker requirement of Disjunctive Rationality. While there are convincing arguments that the rational closure forms the ``simplest'' rational consequence relation extending a given set of conditionals, the question of what is the simplest *disjunctive* consequence relation has not been explored. In this paper, we propose a solution to this question and explore some of its properties.

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Ekramnia, Milad, Jacques Mehler, and Ghislaine Dehaene-Lambertz. "Disjunctive inference in preverbal infants." iScience 25, no. 2 (February 2022): 103817. http://dx.doi.org/10.1016/j.isci.2022.103817.

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Ekramnia, Milad, Jacques Mehler, and Ghislaine Dehaene-Lambertz. "Disjunctive inference in preverbal infants." iScience 24, no. 10 (October 2021): 103203. http://dx.doi.org/10.1016/j.isci.2021.103203.

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Santorio, Paolo. "Simplification is not Scalar Strengthening." Semantics and Linguistic Theory 30 (March 2, 2021): 624. http://dx.doi.org/10.3765/salt.v30i0.4856.

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We show that Simplification of Disjunctive antecedents is not a scalar inference. The argument exploits information-sensitive modals, like epistemic "probably" and deliberative "ought". When items of this sort are the main modal of a conditional, we can have that: (i) If A or B, Mod C is true; (ii) the basic meaning computed via classical semantics for conditionals and disjunction is false. This combination is impossible on any scalar account of Simplification: scalar inferences are strengthenings, hence the output of scalar inferences must entail the basic meaning of a sentence. We suggest an account of Simplification based on alternative semantics, and show how this account can be made compatible with old and new counterexamples to Simplification.

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Ferrigno, Stephen, Yiyun Huang, and Jessica F. Cantlon. "Reasoning Through the Disjunctive Syllogism in Monkeys." Psychological Science 32, no. 2 (January 25, 2021): 292–300. http://dx.doi.org/10.1177/0956797620971653.

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The capacity for logical inference is a critical aspect of human learning, reasoning, and decision-making. One important logical inference is the disjunctive syllogism: given A or B, if not A, then B. Although the explicit formation of this logic requires symbolic thought, previous work has shown that nonhuman animals are capable of reasoning by exclusion, one aspect of the disjunctive syllogism (e.g., not A = avoid empty). However, it is unknown whether nonhuman animals are capable of the deductive aspects of a disjunctive syllogism (the dependent relation between A and B and the inference that “if not A, then B” must be true). Here, we used a food-choice task to test whether monkeys can reason through an entire disjunctive syllogism. Our results show that monkeys do have this capacity. Therefore, the capacity is not unique to humans and does not require language.

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Shen, Yi-Dong, and Thomas Eiter. "Determining inference semantics for disjunctive logic programs." Artificial Intelligence 277 (December 2019): 103165. http://dx.doi.org/10.1016/j.artint.2019.103165.

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Wong, K. "Sound and Complete Inference Rules for SE-Consequence." Journal of Artificial Intelligence Research 31 (January 31, 2008): 205–16. http://dx.doi.org/10.1613/jair.2472.

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The notion of strong equivalence on logic programs with answer set semantics gives rise to a consequence relation on logic program rules, called SE-consequence. We present a sound and complete set of inference rules for SE-consequence on disjunctive logic programs.

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ROBLES, GEMMA, and JOSÉ M. MÉNDEZ. "PARACONSISTENT LOGICS INCLUDED IN LEWIS’ S4." Review of Symbolic Logic 3, no. 3 (July 23, 2010): 442–66. http://dx.doi.org/10.1017/s1755020310000109.

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As is known, a logic S is paraconsistent if the rule ECQ (E contradictione quodlibet) is not a rule of S. Not less well known is the fact that Lewis’ modal logics are not paraconsistent. Actually, Lewis vindicates the validity of ECQ in a famous proof currently known as the “Lewis’ proof” or “Lewis’ argument.” This proof essentially leans on the Disjunctive Syllogism as a rule of inference. The aim of this paper is to define a series of paraconsistent logics included in S4 where the Disjunctive Syllogism is valid only as a rule of proof.

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GRECO, GIANLUIGI, SERGIO GRECO, IRINA TRUBITSYNA, and ESTER ZUMPANO. "Optimization of bound disjunctive queries with constraints." Theory and Practice of Logic Programming 5, no. 6 (October 31, 2005): 713–45. http://dx.doi.org/10.1017/s1471068404002273.

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This paper presents a technique for the optimization of bound queries over disjunctive deductive databases with constraints. The proposed approach is an extension of the well-known Magic-Set technique and is well-suited for being integrated in current bottom-up (stable) model inference engines. More specifically, it is based on the exploitation of binding propagation techniques which reduce the size of the data relevant to answer the query and, consequently, reduces both the complexity of computing a single model and the number of models to be considered. The motivation of this work stems from the observation that traditional binding propagation optimization techniques for bottom-up model generator systems, simulating the goal driven evaluation of top-down engines, are only suitable for positive (disjunctive) queries, while hard problems are expressed using unstratified negation. The main contribution of the paper consists in the extension of a previous technique, defined for positive disjunctive queries, to queries containing both disjunctive heads and constraints (a simple and expressive form of unstratified negation). As the usual way of expressing declaratively hard problems is based on the guess-and-check technique, where the guess part is expressed by means of disjunctive rules and the check part is expressed by means of constraints, the technique proposed here is highly relevant for the optimization of queries expressing hard problems. The value of the technique has been proved by several experiments.

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Pkhakadze, Sopo, and Hans Tompits. "Sequent-Type Calculi for Three-Valued and Disjunctive Default Logic." Axioms 9, no. 3 (July 21, 2020): 84. http://dx.doi.org/10.3390/axioms9030084.

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Default logic is one of the basic formalisms for nonmonotonic reasoning, a well-established area from logic-based artificial intelligence dealing with the representation of rational conclusions, which are characterised by the feature that the inference process may require to retract prior conclusions given additional premisses. This nonmonotonic aspect is in contrast to valid inference relations, which are monotonic. Although nonmonotonic reasoning has been extensively studied in the literature, only few works exist dealing with a proper proof theory for specific logics. In this paper, we introduce sequent-type calculi for two variants of default logic, viz., on the one hand, for three-valued default logic due to Radzikowska, and on the other hand, for disjunctive default logic, due to Gelfond, Lifschitz, Przymusinska, and Truszczyński. The first variant of default logic employs Łukasiewicz’s three-valued logic as the underlying base logic and the second variant generalises defaults by allowing a selection of consequents in defaults. Both versions have been introduced to address certain representational shortcomings of standard default logic. The calculi we introduce axiomatise brave reasoning for these versions of default logic, which is the task of determining whether a given formula is contained in some extension of a given default theory. Our approach follows the sequent method first introduced in the context of nonmonotonic reasoning by Bonatti, which employs a rejection calculus for axiomatising invalid formulas, taking care of expressing the consistency condition of defaults.

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Zhou, Peng, Jacopo Romoli, and Stephen Crain. "Children's knowledge of free choice inferences." Semantics and Linguistic Theory 23 (August 24, 2013): 632. http://dx.doi.org/10.3765/salt.v23i0.2657.

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This paper presents experimental results showing that four-year-old Mandarin- speaking children draw free choice inferences from disjunctive statements, though they are not able to compute inferences of exclusivity for disjunctive statements or other scalar implicatures. The findings connect to those of Chemla & Bott (under review) who report differences in how adults process free choice inferences versus scalar implicatures and, prima facie, the findings pose a challenge to treatments that attempt to unify inferences of both kinds. Instead, the findings appear to favour accounts that invoke different analyses for each kind of inference, such as Zimmerman 2000a, Geurts 2005, and Barker 2010. The results, however, also support the recent approach in the experimental literature which attributes children’s failures to compute scalar implicatures to a difficulty with alternatives: children may lack the lexical knowledge of alternatives, or these implicatures impose such a high processing cost that children are unable to handle the alternatives necessary to compute them (Gualmini, Crain, Meroni, Chierchia & Guasti 2001 Chierchia, Crain, Guasti & Thornton 2001 Reinhart 2006; Barner, Brooks & Bale 2011; Singh, Wexler, Astle, Kamawar & Fox 2012). If accessing alternatives is the source of children’s difficulty, then they would be expected to perform better if the requisite alternatives are made explicit, as sub-strings of the asserted sentences. This is exactly what we found. Children were able to compute free choice inferences based on alternatives that were made explicit in the assertion, but children were unable to compute ‘regular’ scalar implicatures arising from alternatives lacking this property. We discuss the implications of these findings for the debate about the relationship between free choice inferences and scalar implicatures and children’s knowledge of alternatives.

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PRADERA, ANA, ENRIC TRILLAS, and SUSANA CUBILLO. "ON MODUS PONENS GENERATING FUNCTIONS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 08, no. 01 (February 2000): 7–19. http://dx.doi.org/10.1142/s0218488500000034.

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This paper investigates the use of functions other than t-norms to model the Modus Ponens rule in a fuzzy inference process. For that purpose, new definitions for fuzzy inference related concepts are suggested, that take into account the possibility of using a larger class of functions. In particular, the concept of "Modus Ponens generating function" is revisited, allowing to find out when and where (in which subset of the defined universe) an operator is able to generate the Modus Ponens scheme. In addition, given such an operator, the conditional relations that may be used along with it to model an inference process are found. These results are applied to some common operators, finding their Modus Ponens generation capacity as well as their corresponding residuated fuzzy conditionals. Finally, the relation between an operator's ability to describe the Modus Ponens rule and its conjunctive/disjunctive behaviour is also studied, by means of a series of sufficient and/or necessary conditions relating both concepts.

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Aranda, Víctor. "Completud débil y Post completud en la escuela de Hilbert." Humanities Journal of Valparaiso, no. 14 (December 29, 2019): 449. http://dx.doi.org/10.22370/rhv2019iss14pp449-466.

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The aim of this paper is to clarify why propositional logic is Post complete and its weak completeness was almost unnoticed by Hilbert and Bernays, while first-order logic is Post incomplete and its weak completeness was seen as an open problem by Hilbert and Ackermman. Thus, I will compare propositional and first-order logic in the Prinzipien der Mathematik, Bernays’s second Habilitationsschrift and the Grundzüge der Theoretischen Logik. The so called “arithmetical interpretation”, the conjunctive and disjunctive normal forms and the soundness of the propositional rules of inference deserve special emphasis.

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KAFLE, BISHOKSAN, JOHN P. GALLAGHER, GRAEME GANGE, PETER SCHACHTE, HARALD SØNDERGAARD, and PETER J. STUCKEY. "An iterative approach to precondition inference using constrained Horn clauses." Theory and Practice of Logic Programming 18, no. 3-4 (July 2018): 553–70. http://dx.doi.org/10.1017/s1471068418000091.

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AbstractWe present a method for automatic inference of conditions on the initial states of a program that guarantee that the safety assertions in the program are not violated. Constrained Horn clauses (CHCs) are used to model the program and assertions in a uniform way, and we use standard abstract interpretations to derive an over-approximation of the set ofunsafeinitial states. The precondition then is the constraint corresponding to the complement of that set, under-approximating the set ofsafeinitial states. This idea of complementation is not new, but previous attempts to exploit it have suffered from the loss of precision. Here we develop an iterative specialisation algorithm to give more precise, and in some cases optimal safety conditions. The algorithm combines existing transformations, namely constraint specialisation, partial evaluation and a trace elimination transformation. The last two of these transformations perform polyvariant specialisation, leading to disjunctive constraints which improve precision. The algorithm is implemented and tested on a benchmark suite of programs from the literature in precondition inference and software verification competitions.

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Takai, Shigemasa, and Ratnesh Kumar. "A Generalized Framework for Inference-Based Diagnosis of Discrete Event Systems Capturing Both Disjunctive and Conjunctive Decision-Making." IEEE Transactions on Automatic Control 62, no. 6 (June 2017): 2778–93. http://dx.doi.org/10.1109/tac.2016.2624422.

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Zhu, Zhaohui, and Rong Zhang. "An algebraic characterization of equivalent preferential models." Journal of Symbolic Logic 72, no. 3 (September 2007): 803–33. http://dx.doi.org/10.2178/jsl/1191333843.

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AbstractPreferential models is one of the important semantical structures in nonmonotonic logic. This paper aims to establish an isomorphism theorem for preferential models, which gives us a purely algebraic characterization of the equivalence of preferential models. To this end, we present the notions of local similarity and local simulation. Based on these notions, two operators Δ(•) and μ(•) over preferential models are introduced and explored respectively. Together with other two existent operators ρ(•) and ΠD(•), we introduce an operator ∂D(•). Then the isomorphism theorem is obtained in terms of ∂D(•), which asserts that for any two preferential models M1 and M2, they generate the same preferential inference if and only if ∂D(M1) and ∂D(M2) are isomorphic. Based on ∂D(•), we also get an alternative model-theoretical characterization of the well-known postulate Weaken Disjunctive Rationality. Moreover, in the finite language framework, we show that Δ(μ(•)) is competent for the task of eliminating redundancy, and provide a representation result for k-relations.

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Carr, James R., and Eddy D. Deng. "Comparison of two techniques for applying disjunctive kriging: The Gaussian anamorphosis model versus the direct statistical inference of the bivariate distributions." Mathematical Geology 19, no. 1 (January 1987): 57–68. http://dx.doi.org/10.1007/bf01275434.

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López-Astorga, Miguel. "Exclusivity and kinds of models in modulated disjunctive inferences." Nóesis. Revista de Ciencias Sociales y Humanidades 28, no. 1 (January 1, 2019): 185–95. http://dx.doi.org/10.20983/noesis.2019.1.9.

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Germanchuk, M. S. "Solvability of pseudobulous conditional optimization problems of the type of many salesmen." TAURIDA JOURNAL OF COMPUTER SCIENCE THEORY AND MATHEMATICS, no. 4 (49) (2021): 30–55. http://dx.doi.org/10.37279/1729-3901-2020-19-4-30-55.

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Formalizing routing problems of many traveling salesman (mTSP) in complex networks leads to NP-complete pseudobulous conditional optimization problems. The subclasses of polynomially solvable problems are distinguished, for which the elements of the distance matrix satisfy the triangle inequality and other special representations of the original data. The polynomially solvable assignment problem can be used to determine the required number of salesmen and to construct their routes. Uses a subclass of tasks in the form of pseudobulous optimization with disjunctive normal shape (\textit{DNS}) constraints to which the task is reduced mTSP. Problems in this form are polynomially solvable and allow to combine knowledge about network structure, requirements to pass routes by agents (search procedures) and efficient algorithms of logical inference on constraints in the form of \textit{DNS}. This approach is the theoretical justification for the development of multi-agent system management leading to a solution mTSP. Within the framework of intellectual planning, using resources and capabilities, and taking into account the constraints for each agent on the selected clusters of the network, the construction of a common solution for the whole complex network is achieved.

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Hoernle, Nick, Rafael Michael Karampatsis, Vaishak Belle, and Kobi Gal. "MultiplexNet: Towards Fully Satisfied Logical Constraints in Neural Networks." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 5 (June 28, 2022): 5700–5709. http://dx.doi.org/10.1609/aaai.v36i5.20512.

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We propose a novel way to incorporate expert knowledge into the training of deep neural networks. Many approaches encode domain constraints directly into the network architecture, requiring non-trivial or domain-specific engineering. In contrast, our approach, called MultiplexNet, represents domain knowledge as a quantifier-free logical formula in disjunctive normal form (DNF) which is easy to encode and to elicit from human experts. It introduces a latent Categorical variable that learns to choose which constraint term optimizes the error function of the network and it compiles the constraints directly into the output of existing learning algorithms. We demonstrate the efficacy of this approach empirically on several classical deep learning tasks, such as density estimation and classification in both supervised and unsupervised settings where prior knowledge about the domains was expressed as logical constraints. Our results show that the MultiplexNet approach learned to approximate unknown distributions well, often requiring fewer data samples than the alternative approaches. In some cases, MultiplexNet finds better solutions than the baselines; or solutions that could not be achieved with the alternative approaches. Our contribution is in encoding domain knowledge in a way that facilitates inference. We specifically focus on quantifier-free logical formulae that are specified over the output domain of a network. We show that this approach is both efficient and general; and critically, our approach guarantees 100% constraint satisfaction in a network's output.

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COPESTAKE, ANN. "Appendix: Definitions of typed feature structures." Natural Language Engineering 6, no. 1 (March 2000): 109–12. http://dx.doi.org/10.1017/s1351324900002357.

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The LinGO grammar consists of a specification of a type system and of various typed feature structures which are well-formed according to the type system. The typed feature structures function as grammar rules, lexical rules and lexical entries. There are several variant typed feature structure formalisms, with different computational properties, so in this appendix we very briefly specify the version assumed by the LinGO grammar.This appendix is necessarily terse, and is only intended to allow a reader who already has a knowledge of typed feature structures to understand the specific formalism used in the LinGO grammar. The definitions given below basically follow Carpenter (1992), with the notion of type constraint from Copestake (1992). For formal details of typed feature structures in general see Carpenter (1992). A detailed account of the specific assumptions made here is given in Copestake (1999) (See Chapter 4 for an introduction, and Chapter 5 for a semi-formal account.)Note that the LinGO grammar uses a very restricted formalism. For instance, it does not utilize disjunctive feature structures, negation, implication, inequalities, defaults, set-valued features, extensionality or relational constraints. Constraint resolution does not require that every type be made maximally specific, and the type inference system is essentially non-recursive. The recursive power necessary in grammars is explicitly encoded via rules, which are expressed as typed feature structures, but interpreted as phrase structure rules.

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Soh, Takehide, Mutsunori Banbara, and Naoyuki Tamura. "Proposal and Evaluation of Hybrid Encoding of CSP to SAT Integrating Order and Log Encodings." International Journal on Artificial Intelligence Tools 26, no. 01 (February 2017): 1760005. http://dx.doi.org/10.1142/s0218213017600053.

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This paper proposes a new hybrid encoding of finite linear CSP to SAT which integrates order and log encodings. The former maintains bound consistency by unit propagation and works well for constraints consisting of small/middle sized arity and variable domains. The latter generates smaller CNF and works well for constraints consisting of larger sized arity and variable domains but its performance is not good in general because more inference steps are required to ripple carries. This paper describes the first attempt of hybridizing the order and log encodings without channeling constraints. Each variable is encoded by either the order encoding or the log encoding, and each constraint can contain both types of variables. Using the CSP solver competition benchmark consisting of 1458 instances, we made a comparison between the order, log and proposed hybrid encodings. As a result, the hybrid encoding solves the largest number of instances with the shortest CPU time. We also made a comparison with the four state-of-the-art CSP and SMT solvers Mistral, Opturion CPX, Yices, and z3. In this comparison, the hybrid encoding also shows the best performance. Furthermore, we found that the hybrid encoding is especially superior than other solvers for instances containing disjunctive constraints and global constraints — it indeed solves more instances than the virtual best solver consisting of those four state-of-the-art systems.

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Byrne, Ruth M. J., and P. N. Johnson-Laird. "The Spontaneous Use of Propositional Connectives." Quarterly Journal of Experimental Psychology Section A 45, no. 1 (July 1992): 89–110. http://dx.doi.org/10.1080/14640749208401317.

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We extend the model theory of reasoning to the understanding and use of propositional connectives, such as and, or, and if. We use a novel paraphrase paradigm to compare the model theory to an alternative one based on rules of inference. In Experiment 1, subjects paraphrased pairs of conditionals. Their general knowledge guided their combination of the antecedents: they used disjunctive descriptions to combine antecedents that were each sufficient to bring about the outcome, and they used conjunctive descriptions to combine antecedents that were both necessary to bring about the outcome. They expressed their combinations using simple connectives such as and or or, as the model theory predicts, rather than hypothetical connectives, such as and if or or if, as the rule theory predicts. Experiment 2 demonstrated the phenomenon in the less constrained task of combining three assertions in a single conditional. Conjunctions and disjunctions are easy to elicit; conditionals have proved far more difficult. The model theory proposes that individuals represent a conditional situation by keeping in mind the described events, but they also keep in mind that there may be alternatives to the events. Therefore, they should use conditionals when they are aware that the events may or may not occur. Experiment 3 corroborated this prediction: subjects used conditionals to combine assertions (with no restrictions on the connective they should use) when the clause describing the outcome contained a modal verb that suggested that the outcome might or might not occur.

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Giunchiglia, E., M. Narizzano, and A. Tacchella. "Clause/Term Resolution and Learning in the Evaluation of Quantified Boolean Formulas." Journal of Artificial Intelligence Research 26 (August 17, 2006): 371–416. http://dx.doi.org/10.1613/jair.1959.

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Resolution is the rule of inference at the basis of most procedures for automated reasoning. In these procedures, the input formula is first translated into an equisatisfiable formula in conjunctive normal form (CNF) and then represented as a set of clauses. Deduction starts by inferring new clauses by resolution, and goes on until the empty clause is generated or satisfiability of the set of clauses is proven, e.g., because no new clauses can be generated. In this paper, we restrict our attention to the problem of evaluating Quantified Boolean Formulas (QBFs). In this setting, the above outlined deduction process is known to be sound and complete if given a formula in CNF and if a form of resolution, called ``Q-resolution'', is used. We introduce Q-resolution on terms, to be used for formulas in disjunctive normal form. We show that the computation performed by most of the available procedures for QBFs --based on the Davis-Logemann-Loveland procedure (DLL) for propositional satisfiability-- corresponds to a tree in which Q-resolution on terms and clauses alternate. This poses the theoretical bases for the introduction of learning, corresponding to recording Q-resolution formulas associated with the nodes of the tree. We discuss the problems related to the introduction of learning in DLL based procedures, and present solutions extending state-of-the-art proposals coming from the literature on propositional satisfiability. Finally, we show that our DLL based solver extended with learning, performs significantly better on benchmarks used in the 2003 QBF solvers comparative evaluation.

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JI, JIANMIN, FANGFANG LIU, and JIA-HUAI YOU. "Well-founded operators for normal hybrid MKNF knowledge bases." Theory and Practice of Logic Programming 17, no. 5-6 (September 2017): 889–905. http://dx.doi.org/10.1017/s1471068417000291.

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AbstractHybrid MKNF knowledge bases have been considered one of the dominant approaches to combining open world ontology languages with closed world rule-based languages. Currently, the only known inference methods are based on the approach of guess-and-verify, while most modern SAT/ASP solvers are built under the DPLL architecture. The central impediment here is that it is not clear what constitutes a constraint propagator, a key component employed in any DPLL-based solver. In this paper, we address this problem by formulating the notion of unfounded sets for non-disjunctive hybrid MKNF knowledge bases, based on which we propose and study two new well-founded operators. We show that by employing a well-founded operator as a constraint propagator, a sound and complete DPLL search engine can be readily defined. We compare our approach with the operator based on the alternating fixpoint construction by Knorr et al. (2011. Artificial Intelligence 175, 9, 1528–1554) and show that, when applied to arbitrary partial partitions, the new well-founded operators not only propagate more truth values but also circumvent the non-converging behavior of the latter. In addition, we study the possibility of simplifying a given hybrid MKNF knowledge base by employing a well-founded operator and show that, out of the two operators proposed in this paper, the weaker one can be applied for this purpose and the stronger one cannot. These observations are useful in implementing a grounder for hybrid MKNF knowledge bases, which can be applied before the computation of MKNF models.

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García-Madruga, Juan A., Francisco Gutiérrez, Nuria Carriedo, Sergio Moreno, and Philip N. Johnson-Laird. "Mental Models in Deductive Reasoning." Spanish Journal of Psychology 5, no. 2 (November 2002): 125–40. http://dx.doi.org/10.1017/s1138741600005904.

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We report research investigating the role of mental models in deduction. The first study deals with conjunctive inferences (from one conjunction and two conditional premises) and disjunctive inferences (from one disjunction and the same two conditionals). The second study examines reasoning from multiple conditionals such as: If e then b; If a then b; If b then c; What follows between a and c? The third study addresses reasoning from different sorts of conditional assertions, including conditionals based on if then, only if, and unless. The paper also presents research on figural effects in syllogistic reasoning, on the effects of structure and believability in reasoning from double conditionals, and on reasoning from factual, counterfactual, and semifactual conditionals. The findings of these studies support the model theory, pose some difficulties for rule theories, and show the influence on reasoning of the linguistic structure and the semantic content of problems.

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Sahu, Abhijeet, and Katherine Davis. "Inter-Domain Fusion for Enhanced Intrusion Detection in Power Systems: An Evidence Theoretic and Meta-Heuristic Approach." Sensors 22, no. 6 (March 9, 2022): 2100. http://dx.doi.org/10.3390/s22062100.

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False alerts due to misconfigured or compromised intrusion detection systems (IDS) in industrial control system (ICS) networks can lead to severe economic and operational damage. However, research using deep learning to reduce false alerts often requires the physical and cyber sensor data to be trustworthy. Implicit trust is a major problem for artificial intelligence or machine learning (AI/ML) in cyber-physical system (CPS) security, because when these solutions are most urgently needed is also when they are most at risk (e.g., during an attack). To address this, the Inter-Domain Evidence theoretic Approach for Inference (IDEA-I) is proposed that reframes the detection problem as how to make good decisions given uncertainty. Specifically, an evidence theoretic approach leveraging Dempster–Shafer (DS) combination rules and their variants is proposed for reducing false alerts. A multi-hypothesis mass function model is designed that leverages probability scores obtained from supervised-learning classifiers. Using this model, a location-cum-domain-based fusion framework is proposed to evaluate the detector’s performance using disjunctive, conjunctive, and cautious conjunctive rules. The approach is demonstrated in a cyber-physical power system testbed, and the classifiers are trained with datasets from Man-In-The-Middle attack emulation in a large-scale synthetic electric grid. For evaluating the performance, we consider plausibility, belief, pignistic, and general Bayesian theorem-based metrics as decision functions. To improve the performance, a multi-objective-based genetic algorithm is proposed for feature selection considering the decision metrics as the fitness function. Finally, we present a software application to evaluate the DS fusion approaches with different parameters and architectures.

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Khemlani, Sangeet, and P. N. Johnson-Laird. "Disjunctive illusory inferences and how to eliminate them." Memory & Cognition 37, no. 5 (July 2009): 615–23. http://dx.doi.org/10.3758/mc.37.5.615.

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Chevallier, Coralie, Ira A. Noveck, Tatjana Nazir, Lewis Bott, Valentina Lanzetti, and Dan Sperber. "Making disjunctions exclusive." Quarterly Journal of Experimental Psychology 61, no. 11 (November 2008): 1741–60. http://dx.doi.org/10.1080/17470210701712960.

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This work examines how people interpret the sentential connective “or”, which can be viewed either inclusively (A or B or both) or exclusively (A or B but not both). Following up on prior work concerning quantifiers (Bott & Noveck, 2004; Noveck, 2001; Noveck & Posada, 2003), which shows that the common pragmatic interpretation of “some”, some but not all, is conveyed as part of an effortful step, we investigate how extra effort applied to disjunctive statements leads to a pragmatic interpretation of “or”, or but not both. Experiment 1 compelled participants to wait for three seconds before answering, hence giving them the opportunity to process the utterance more deeply. Experiments 2 and 3 emphasized “or”, either by visual means (“OR”) or by prosodic means (contrastive stress) as another way to encourage participants to apply more effort. Following a relevance-theoretic line of argument, we hypothesized that conditions encouraging more processing effort would give rise to more pragmatic inferences and hence to more exclusive interpretations of the disjunction. This prediction was confirmed in the three experiments.

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García-Madruga, J. A., S. Moreno, N. Carriedo, F. Gutiérrez, and P. N. Johnson-Laird. "Are Conjunctive Inferences Easier than Disjunctive Inferences? A Comparison of Rules and Models." Quarterly Journal of Experimental Psychology Section A 54, no. 2 (May 2001): 613–32. http://dx.doi.org/10.1080/713755974.

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Bayırlı, İsa Kerem. "Exclusive Free Choice in Turkish." Proceedings of the Workshop on Turkic and Languages in Contact with Turkic 6, no. 1 (December 19, 2021): 5050. http://dx.doi.org/10.3765/ptu.v6i1.5050.

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In this paper, we will be concerned with a type of interpretation associated with ya…ya… disjunction in Turkish where the Free-Choice inference is obligatorily accompanied with the Prohibition inference. We claim that such a reading arises as a consequence of the fact that each disjunct inside ya…ya… disjunction is parsed with only (overt or covert). We show that the scalar nature of only, which we model as a restriction on alternatives, is crucial in accounting for the exclusive Free-Choice readings. We finally discuss some differences between only and the Exh operator

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Citkin, Alex. "Deductive Systems with Multiple-Conclusion Rules and the Disjunction Property." Axioms 8, no. 3 (August 30, 2019): 100. http://dx.doi.org/10.3390/axioms8030100.

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Using the defined notion of the inference with multiply-conclusion rules, we show that in the logics enjoying the disjunction property, any derivable rule can be inferred from the single-conclusion rules and a single multiple-conclusion rule, which represents the disjunction property. Also, the conversion algorithm of single- and multiple-conclusion deductive systems into each other is studied.

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García-Madruga, Juan A., Nuria Carriedo, and Sergio Moreno-Ríos. "The Semantics of ‘unless’ Conditionals: Evidence from ‘unless’ and Disjunctive Inferences." Spanish journal of psychology 14, no. 2 (November 2011): 569–79. http://dx.doi.org/10.5209/rev_sjop.2011.v14.n2.5.

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We report the results of an experiment investigating conditional inferences from conditional assertions such as ‘Juan won't go to León unless Nuria goes to Madrid’ and ‘Either Nuria goes to Madrid or Juan won't go to León’. This experiment addresses Dancygier's claims about the semantics of ‘unless’ by examining inferential endorsements of ‘not-A unless B’ and ‘Either B or not-A’ in the canonical order, presenting the categorical premise after the conditional assertions, and in the inverse order, presenting the categorical premise before the conditional assertions. The results of the experiment confirm that the representation of ‘unless’ includes two possibilities, although as Dancygier holds one of the possibilities may not be complete. The implications of the results are discussed in the context of the strategic nature of conditional reasoning and recent convergent theories of linguistic processing.

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Klauer, Karl Christoph, and Klaus Oberauer. "Testing the Mental Model Theory of Propositional Reasoning." Quarterly Journal of Experimental Psychology Section A 48, no. 3 (August 1995): 671–87. http://dx.doi.org/10.1080/14640749508401410.

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Johnson-Laird, Byrne, and Schaeken (1992) present a theory of propositional reasoning by mental models. The present study provides a comprehensive test of the predictions of that theory for the difficulty of simple disjunctive and conditional inferences. The results are largely consistent with the complex pattern of predictions. They are discussed in the light of recently proposed modifications of the original theory.

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Champollion, Lucas, Anna Alsop, and Ioana Grosu. "Free choice disjunction as a rational speech act." Semantics and Linguistic Theory 29 (December 9, 2019): 238. http://dx.doi.org/10.3765/salt.v29i0.4608.

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The so-called free choice inference (from You may take an apple or a pear to You may take an apple) is mysterious because it does not follow from ordinary modal logic. We show that this inference arises in the Rational Speech Act framework (Frank & Goodman 2012). Our basic idea is inspired by exhaustification-based models of free choice (Fox 2007) and by game-theoretic accounts based on iterated best response (Franke 2011). We assume that when the speaker utters You may take an apple or a pear, the hearer reasons about why the speaker did not choose alternative utterances such as You may take an apple. A crucial ingredient in our explanation is the idea of semantic uncertainty (Bergen, Levy & Goodman 2016). Specifically, we assume that the speaker is uncertain whether or not the hearer will interpret You may take an apple as forbidding them from taking a pear. This uncertainty can be thought of as resulting from Fox’s (2007) optional covert exhaustification. Uttering the disjunction is a way for the speaker to prevent the hearer from concluding that any fruit is forbidden to take. Knowing this, the hearer concludes that they may choose either fruit.

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Prado, Jérôme, Nicola Spotorno, Eric Koun, Emily Hewitt, Jean-Baptiste Van der Henst, Dan Sperber, and Ira A. Noveck. "Neural Interaction between Logical Reasoning and Pragmatic Processing in Narrative Discourse." Journal of Cognitive Neuroscience 27, no. 4 (April 2015): 692–704. http://dx.doi.org/10.1162/jocn_a_00744.

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Logical connectives (e.g., or, if, and not) are central to everyday conversation, and the inferences they generate are made with little effort in pragmatically sound situations. In contrast, the neural substrates of logical inference-making have been studied exclusively in abstract tasks where pragmatic concerns are minimal. Here, we used fMRI in an innovative design that employed narratives to investigate the interaction between logical reasoning and pragmatic processing in natural discourse. Each narrative contained three premises followed by a statement. In Fully-deductive stories, the statement confirmed a conclusion that followed from two steps of disjunction–elimination (e.g., Xavier considers Thursday, Friday, or Saturday for inviting his girlfriend out; he removes Thursday before he rejects Saturday and declares “I will invite her out for Friday”). In Implicated-premise stories, an otherwise identical narrative included three premises that twice removed a single option from consideration (i.e., Xavier rejects Thursday for two different reasons). The conclusion therefore necessarily prompts an implication (i.e., Xavier must have removed Saturday from consideration as well). We report two main findings. First, conclusions of Implicated-premise stories are associated with more activity than conclusions of Fully-deductive stories in a bilateral frontoparietal system, suggesting that these regions play a role in inferring an implicated premise. Second, brain connectivity between these regions increases with pragmatic abilities when reading conclusions in Implicated-premise stories. These findings suggest that pragmatic processing interacts with logical inference-making when understanding arguments in narrative discourse.

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Parreaux, Lionel, and Chun Yin Chau. "MLstruct: principal type inference in a Boolean algebra of structural types." Proceedings of the ACM on Programming Languages 6, OOPSLA2 (October 31, 2022): 449–78. http://dx.doi.org/10.1145/3563304.

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Intersection and union types are becoming more popular by the day, entering the mainstream in programming languages like TypeScript and Scala 3. Yet, no language so far has managed to combine these powerful types with principal polymorphic type inference. We present a solution to this problem in MLstruct, a language with subtyped records, equirecursive types, first-class unions and intersections, class-based instance matching, and ML-style principal type inference. While MLstruct is mostly structurally typed, it contains a healthy sprinkle of nominality for classes, which gives it desirable semantics, enabling the expression of a powerful form of extensible variants that does not need row variables. Technically, we define the constructs of our language using conjunction, disjunction, and negation connectives, making sure they form a Boolean algebra, and we show that the addition of a few nonstandard but sound subtyping rules gives us enough structure to derive a sound and complete type inference algorithm. With this work, we hope to foster the development of better type inference for present and future programming languages with expressive subtyping systems.

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Essayagh, Benjamin, Francesca Mantovani, Giovanni Benfari, and Maurice Enriquez-Sarano. "Of Causality and Inferences: Mitral Annular Disjunction and Its Consequences—Reply." Journal of the American Society of Echocardiography 35, no. 2 (February 2022): 239–41. http://dx.doi.org/10.1016/j.echo.2021.11.006.

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Gotzner, Nicole, David Barner, and Stephen Crain. "Disjunction Triggers Exhaustivity Implicatures in 4- to 5-Year-Olds: Investigating the Role of Access to Alternatives." Journal of Semantics 37, no. 2 (April 11, 2020): 219–45. http://dx.doi.org/10.1093/jos/ffz021.

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Abstract Children’s difficulty deriving scalar implicatures has been attributed to a variety of factors including processing limitations, an inability to access scalar alternatives, and pragmatic tolerance. The present research explores the nature of children’s difficulty by investigating a previously unexplored kind of inference—an exhaustivity implicature that is triggered by disjunction. We reasoned that if children are able to draw quantity implicatures but have difficulties accessing alternative lexical expressions from a scale, then they should perform better on exhaustivity implicatures than on scalar implicatures, since the former do not require spontaneously accessing relevant scalar alternatives from the lexicon. We conducted two experiments. Experiment 1 found that 4- to 5-year-olds consistently computed exhaustivity implicatures to a greater extent than scalar implicatures. Experiment 2 demonstrated that children are more likely to compute exhaustivity implicatures with disjunction compared to conjunction. We conclude that children often fail to derive scalar implicatures because (1) they struggle to access scalar alternatives and (2) disjunction (but not conjunction) makes subdomain alternatives particularly salient. Thus, the findings suggest that exhaustivity implicatures can be derived without reference to a scale of alternatives.

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Barrouillet, Pierre, and Jean-François Lecas. "Illusory inferences from a disjunction of conditionals: a new mental models account." Cognition 76, no. 2 (August 2000): 167–73. http://dx.doi.org/10.1016/s0010-0277(00)00075-5.

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Joksimović, Marija Boričić. "On Basic Probability Logic Inequalities." Mathematics 9, no. 12 (June 17, 2021): 1409. http://dx.doi.org/10.3390/math9121409.

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We give some simple examples of applying some of the well-known elementary probability theory inequalities and properties in the field of logical argumentation. A probabilistic version of the hypothetical syllogism inference rule is as follows: if propositions A, B, C, A→B, and B→C have probabilities a, b, c, r, and s, respectively, then for probability p of A→C, we have f(a,b,c,r,s)≤p≤g(a,b,c,r,s), for some functions f and g of given parameters. In this paper, after a short overview of known rules related to conjunction and disjunction, we proposed some probabilized forms of the hypothetical syllogism inference rule, with the best possible bounds for the probability of conclusion, covering simultaneously the probabilistic versions of both modus ponens and modus tollens rules, as already considered by Suppes, Hailperin, and Wagner.

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Cherubini, Paolo, Alberto Mazzocco, and Stefano Minelli. "Facilitation and inhibition caused by the orienting of attention in propositional reasoning tasks." Quarterly Journal of Experimental Psychology 60, no. 11 (October 2007): 1496–523. http://dx.doi.org/10.1080/17470210601066103.

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In an attempt to study the orienting of attention in reasoning, we developed a set of propositional reasoning tasks structurally similar to Posner's (1980) spatial cueing paradigm, widely used to study the orienting of attention in perceptual tasks. We cued the representation in working memory of a reasoning premise, observing whether inferences drawn using that premise or a different, uncued one were facilitated, hindered, or unaffected. The results of Experiments 1a, 1b, 1c, and 1d, using semantically (1a–1c) or statistically (1d) informative cues, showed a robust, long-lasting facilitation for drawing inferences from the cued rule. In Experiment 2, using uninformative cues, inferences from the cued rule were facilitated with a short stimulus onset asynchrony (SOA), whereas they were delayed when the SOA was longer, an effect that is similar to the “inhibition of return” (IOR) in perceptual tasks. Experiment 3 used uninformative cues, three different SOAs, and inferential rules with disjunctive antecedents, replicating the IOR-like effect with the long SOAs and, at the short SOA, finding evidence of a gradient-like behaviour of the facilitation effect. Our findings show qualitative similarities to some effects typically observed in the orienting of visual attention, although the tasks did not involve spatial orienting.

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Sgurev, V. "An Essay on Complex Valued Propositional Logic." Information Technologies and Control 11, no. 1 (March 1, 2013): 2–7. http://dx.doi.org/10.2478/itc-2013-0001.

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Abstract In decision making logic it is often necessary to solve logical equations for which, due to the features of disjunction and conjunction, no admissible solutions exist. In this paper an approach is suggested, in which by the introduction of Imaginary Logical Variables (ILV), the classical propositional logic is extended to a complex one. This provides a possibility to solve a large class of logical equations.The real and imaginary variables each satisfy the axioms of Boolean algebra and of the lattice. It is shown that the Complex Logical Variables (CLV) observe the requirements of Boolean algebra and the lattice axioms. Suitable definitions are found for these variables for the operations of disjunction, conjunction, and negation. A series of results are obtained, including also the truth tables of the operations disjunction, conjunction, negation, implication, and equivalence for complex variables. Inference rules are deduced for them analogous to Modus Ponens and Modus Tollens in the classical propositional logic. Values of the complex variables are obtained, corresponding to TRUE (T) and FALSE (F) in the classic propositional logic. A conclusion may be made from the initial assumptions and the results achieved, that the imaginary logical variable i introduced hereby is “truer” than condition “T” of the classic propositional logic and i - “falser” than condition “F”, respectively. Possibilities for further investigations of this class of complex logical structures are pointed out

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Martínez, José Felipe, Jonathan Schweig, and Pete Goldschmidt. "Approaches for Combining Multiple Measures of Teacher Performance." Educational Evaluation and Policy Analysis 38, no. 4 (September 23, 2016): 738–56. http://dx.doi.org/10.3102/0162373716666166.

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A key question facing teacher evaluation systems is how to combine multiple measures of complex constructs into composite indicators of performance. We use data from the Measures of Effective Teaching (MET) study to investigate the measurement properties of composite indicators obtained under various conjunctive, disjunctive (or complementary), and weighted (or compensatory) models. We find that accuracy varies across models and cut-scores and that models with similar accuracy may yield different teacher classifications. Accuracy and consistency are greatest if composites are constructed to maximize reliability and lowest if they seek to optimally predict student test scores. We discuss the implications of the results for the validity of inferences about the performance of individual teachers, and more generally for the design of teacher evaluation systems.

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Ninan, Dilip. "The Projection Problem for Predicates of Taste." Semantics and Linguistic Theory 30 (March 2, 2021): 753. http://dx.doi.org/10.3765/salt.v30i0.4809.

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Utterances of simple sentences containing taste predicates (e.g. "delicious", "fun", "frightening") typically imply that the speaker has had a particular sort of first-hand experience with the object of predication. For example, an utterance of "The carrot cake is delicious" would typically imply that the speaker had actually tasted the cake in question, and is not, for example, merely basing her judgment on the testimony of others. According to one approach, this 'acquaintance inference' is essentially an implicature, one generated by the Maxim of Quality together with a certain principle concerning the epistemology of taste (Ninan 2014). We first discuss some problems for this approach, problems that arise in connection with disjunction and generalized quantifiers. Then, after stating a conjecture concerning which operators 'obviate' the acquaintance inference and which do not, we build on Anand and Korotkova 2018 and Willer and Kennedy Forthcoming by developing a theory that treats the acquaintance requirement as a presupposition, albeit one that can be obviated by certain operators.

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DZIK, WOJCIECH, and PIOTR WOJTYLAK. "UNIFICATION IN SUPERINTUITIONISTIC PREDICATE LOGICS AND ITS APPLICATIONS." Review of Symbolic Logic 12, no. 1 (December 3, 2018): 37–61. http://dx.doi.org/10.1017/s1755020318000011.

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AbstractWe introduce unification in first-order logic. In propositional logic, unification was introduced by S. Ghilardi, see Ghilardi (1997, 1999, 2000). He successfully applied it in solving systematically the problem of admissibility of inference rules in intuitionistic and transitive modal propositional logics. Here we focus on superintuitionistic predicate logics and apply unification to some old and new problems: definability of disjunction and existential quantifier, disjunction and existential quantifier under implication, admissible rules, a basis for the passive rules, (almost) structural completeness, etc. For this aim we apply modified specific notions, introduced in propositional logic by Ghilardi, such as projective formulas, projective unifiers, etc.Unification in predicate logic seems to be harder than in the propositional case. Any definition of the key concept of substitution for predicate variables must take care of individual variables. We allow adding new free individual variables by substitutions (contrary to Pogorzelski & Prucnal (1975)). Moreover, since predicate logic is not as close to algebra as propositional logic, direct application of useful algebraic notions of finitely presented algebras, projective algebras, etc., is not possible.

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Schaeken, Walter, Philip N. Johnson-Laird, Ruth M. J. Byrne, and Gery D’Ydewalle. "A Comparison of Conditional and Disjunctive Inferences: A Case Study of the Mental Model Theory of Reasoning." Psychologica Belgica 35, no. 1 (January 1, 1995): 57. http://dx.doi.org/10.5334/pb.877.

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Chagrov, Alexander, and Michael Zakharyaschev. "The undecidability of the disjunction property of propositional logics and other related problems." Journal of Symbolic Logic 58, no. 3 (September 1993): 967–1002. http://dx.doi.org/10.2307/2275108.

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‘How can we recognize, given axioms and inference rules of a calculus, whether the calculus has such-and-such property?’ A question of this kind arises whenever we deal with a new logic system. For large families of logics, this question may be considered as an algorithmic problem, and a property is called decidable in a given family if there exists an algorithm which is capable of deciding, for a finite axiomatics of a calculus in the family, whether or not it has the property.In the class of intermediate propositional logics, for instance, nontrivial properties such as the tabularity, pretabularity, and interpolation property (Maksimova [1972, 1977]) are decidable. However, for many other important properties—decidability, finite model property, disjunction property, Halldén-completeness, etc.—effective criteria were not found in spite of considerable efforts.In this paper we show that the difficulties in investigating these properties in the classes of intermediate logics and normal modal logics containing S4 are of principal nature, since all of them turn out to be algorithmically undecidable. In other words, there are no algorithms which, given a finite set of axioms of an intermediate or modal calculus, can recognize whether or not it is decidable, Halldén-complete, has the finite model or disjunction property.The first results concerning the undecidability of properties of calculi seem to have been obtained by Linial and Post [1949], who proved the undecidability of the problem of equivalence to classical calculus in the class of all propositional calculi with the same language as the classical one and the two inference rules: modus ponens and substitution. Kuznetsov [1963] generalized this result having proved the undecidability of the problem of equivalence to any fixed intermediate calculus (for instance, to intuitionistic calculus or even the inconsistent one). However, these results will not hold if we confine ourselves only to the class of intermediate logics, though the problem of equivalence to the undecidable intermediate calculus of Shehtman [1978] is clearly undecidable in this class as well.

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Tieu, Lyn, Cory Bill, and Jacopo Romoli. "Homogeneity or implicature: An experimental investigation of free choice." Semantics and Linguistic Theory 29 (December 17, 2019): 706. http://dx.doi.org/10.3765/salt.v29i0.4631.

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A sentence containing disjunction in the scope of a possibility modal, such as Angie is allowed to buy the boat or the car, gives rise to the FREE CHOICE inference that Angie can freely choose between the two. This inference poses a well-known puzzle, in that it is not predicted by a standard treatment of modals and disjunction (e.g., Kamp 1974). To complicate things further, FREE CHOICE tends to disappear under negation: Angie is not allowed to buy the boat or the car doesn’t merely convey the negation of free choice, but rather the stronger DUAL PROHIBITION reading that Angie cannot buy either one. There are two main approaches to the FREE CHOICE-DUAL PROHIBITION pattern in the literature. While they both capture the relevant data points, they make a testable, divergent prediction regarding the status of positive and negative sentences in a context in which Angie can only buy one of the two objects, e.g., the boat. In particular, the implicature-based approach (e.g., Fox 2007; Klinedinst 2007; Bar-Lev & Fox 2017) predicts that the positive sentence is true in such a context, but associated with a false implicature, while it predicts the negative sentence to be straightforwardly false. The alternative approach (e.g., Aloni 2018; Goldstein 2018; Willer 2017) predicts both the positive and negative sentences to be equally undefined. Investigating the contrast between these sentences in such a context therefore provides a clear way to address the debate between implicature and non-implicature accounts of FREE CHOICE. We present an experiment aiming to do just this, the results of which present a challenge for the implicature approach. We further discuss how the implicature approach could in theory be developed to account for our results, based on a recent proposal by Enguehard & Chemla (2018) on the distribution of implicatures.

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Journal articles on the topic 'Disjunctive inference'

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