Journal articles: 'Logical entailment'

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Zhou, Y., and Y. Zhang. "A Logical Study of Partial Entailment." Journal of Artificial Intelligence Research 40 (January 20, 2011): 25–56. http://dx.doi.org/10.1613/jair.3117.

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We introduce a novel logical notion--partial entailment--to propositional logic. In contrast with classical entailment, that a formula P partially entails another formula Q with respect to a background formula set \Gamma intuitively means that under the circumstance of \Gamma, if P is true then some "part" of Q will also be true. We distinguish three different kinds of partial entailments and formalize them by using an extended notion of prime implicant. We study their semantic properties, which show that, surprisingly, partial entailments fail for many simple inference rules. Then, we study the related computational properties, which indicate that partial entailments are relatively difficult to be computed. Finally, we consider a potential application of partial entailments in reasoning about rational agents.

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De Bruijn, J., and S. Heymans. "Logical Foundations of RDF(S) with Datatypes." Journal of Artificial Intelligence Research 38 (August 20, 2010): 535–68. http://dx.doi.org/10.1613/jair.3088.

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The Resource Description Framework (RDF) is a Semantic Web standard that provides a data language, simply called RDF, as well as a lightweight ontology language, called RDF Schema. We investigate embeddings of RDF in logic and show how standard logic programming and description logic technology can be used for reasoning with RDF. We subsequently consider extensions of RDF with datatype support, considering D entailment, defined in the RDF semantics specification, and D* entailment, a semantic weakening of D entailment, introduced by ter Horst. We use the embeddings and properties of the logics to establish novel upper bounds for the complexity of deciding entailment. We subsequently establish two novel lower bounds, establishing that RDFS entailment is PTime-complete and that simple-D entailment is coNP-hard, when considering arbitrary datatypes, both in the size of the entailing graph. The results indicate that RDFS may not be as lightweight as one may expect.

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TATAR, DOINA, ANDREEA MIHIS, DANA LUPSA, and EMMA TAMAIANU-MORITA. "ENTAILMENT-BASED LINEAR SEGMENTATION IN SUMMARIZATION." International Journal of Software Engineering and Knowledge Engineering 19, no. 08 (December 2009): 1023–38. http://dx.doi.org/10.1142/s0218194009004520.

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This paper presents some original methods for text summarization of a single source document by extraction. The methods are based on some of our own text segmentation algorithms. We denote them as logical segmentation because for all these methods (LTT, ArcInt and ArcReal) the score of a sentence is calculated starting from the number of sentences which are entailed by it. For a text (which is a sequence of sentences) the scores form a structure which indicates how the most important sentences alternate with less important ones and organizes the text according to its logical content. The second logical method, Pure Entailment also uses definition of the relation of entailment between two texts. At least to our knowledge, it is for the first time that the relation of Text Entailment between the sentences of a text is used for segmentation and summarization. The third original method applies Dynamic Programming and centering theory to the sentences logically scored as above. The obtained ranked logical segments are used in the summarization. Our methods of segmentation and summarization are applied and evaluated against a manually realized segmentation and summarization of the same text by Donald Richie, "The Koan".

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PALOMINO, MIGUEL. "A comparison between two logical formalisms for rewriting." Theory and Practice of Logic Programming 7, no. 1-2 (January 2007): 183–213. http://dx.doi.org/10.1017/s1471068406002845.

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AbstractMeseguer's rewriting logic and the rewriting logic CRWL are two well-known approaches to rewriting as logical deduction that, despite some clear similarities, were designed with different objectives. Here we study the relationships between them, both at a syntactic and at a semantic level. Even though it is not possible to establish an entailment system map between them, both can be naturally simulated in each other. Semantically, there is no embedding between the corresponding institutions. Along the way, the notions of entailment and satisfaction in Meseguer's rewriting logic are generalized.

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Cropper, Andrew, and Sophie Tourret. "Logical reduction of metarules." Machine Learning 109, no. 7 (November 20, 2019): 1323–69. http://dx.doi.org/10.1007/s10994-019-05834-x.

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AbstractMany forms of inductive logic programming (ILP) use metarules, second-order Horn clauses, to define the structure of learnable programs and thus the hypothesis space. Deciding which metarules to use for a given learning task is a major open problem and is a trade-off between efficiency and expressivity: the hypothesis space grows given more metarules, so we wish to use fewer metarules, but if we use too few metarules then we lose expressivity. In this paper, we study whether fragments of metarules can be logically reduced to minimal finite subsets. We consider two traditional forms of logical reduction: subsumption and entailment. We also consider a new reduction technique called derivation reduction, which is based on SLD-resolution. We compute reduced sets of metarules for fragments relevant to ILP and theoretically show whether these reduced sets are reductions for more general infinite fragments. We experimentally compare learning with reduced sets of metarules on three domains: Michalski trains, string transformations, and game rules. In general, derivation reduced sets of metarules outperform subsumption and entailment reduced sets, both in terms of predictive accuracies and learning times.

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Qiu, Junming, Wenqing Li, Zhanhao Xiao, Quanlong Guan, Liangda Fang, Zhao-Rong Lai, and Qian Dong. "Knowledge Compilation Meets Logical Separability." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 5 (June 28, 2022): 5851–60. http://dx.doi.org/10.1609/aaai.v36i5.20529.

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Knowledge compilation is an alternative solution to address demanding reasoning tasks with high complexity via converting knowledge bases into a suitable target language. Interestingly, the notion of logical separability, proposed by Levesque, offers a general explanation for the tractability of clausal entailment for two remarkable languages: decomposable negation normal form and prime implicates. It is interesting to explore what role logical separability on earth plays in problem tractability. In this paper, we apply the notion of logical separability in three reasoning problems within the context of propositional logic: satisfiability check (CO), clausal entailment check (CE) and model counting (CT), contributing to three corresponding polytime procedures. We provide three logical separability based properties: CO- logical separability, CE-logical separability and CT-logical separability. We then identify three novel normal forms: CO-LSNNF, CE-LSNNF and CT-LSNNF based on the above properties. Besides, we show that every normal form is the necessary and sufficient condition under which the corresponding procedure is correct. We finally integrate the above four normal forms into the knowledge compilation map.

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Zaitsev, Dmitry. "Supervenience, Entailment, and Vague Objects." Aitías, Revista de Estudios Filosóficos del Centro de Estudios Humanísticos de la UANL 2, no. 3 (July 1, 2022): 1–20. http://dx.doi.org/10.29105/aitas2.3-27.

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Not long ago came into common use, the relation of supervenience is rapidly gaining in popularity. At the same time, its logical nature, in particular its possible correlations with such fundamental logical relation as entailment, remains unresolved and needs clarification. In this paper, I compare these two relations and outline a new approach to formal explication of supervenience. In so doing, I employ as main sources two conceptions: of intensional semantics, and impossible object descriptions as its core part, introduced in section 3, and of relevant consequence relation, briefly described in section 4, where I also delineate a new entailment interpretation of supevenience. Thus, quite naturally we arrive at contradictory and incomplete descriptions of objects, and that way, uncertainty comes into play. Equally, it allows to propose a tentative definition of supervenience without referring to the terminology of the possible worlds semantics.

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Huang, Xuejing, and Bruno C. d. S. Oliveira. "Distributing intersection and union types with splits and duality (functional pearl)." Proceedings of the ACM on Programming Languages 5, ICFP (August 22, 2021): 1–24. http://dx.doi.org/10.1145/3473594.

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Subtyping with intersection and union types is nowadays common in many programming languages. From the perspective of logic, the subtyping problem is essentially the problem of determining logical entailment : does a logical statement follow from another one? Unfortunately, algorithms for deciding subtyping and logical entailment with intersections, unions and various distributivity laws can be highly non-trivial. This functional pearl presents a novel algorithmic formulation for subtyping (and logical entailment) in the presence of various distributivity rules between intersections, unions and implications (i.e. function types). Unlike many existing algorithms which first normalize types and then apply a subtyping algorithm on the normalized types, our new subtyping algorithm works directly on source types. Our algorithm is based on two recent ideas: a generalization of subtyping based on the duality of language constructs called duotyping ; and splittable types , which characterize types that decompose into two simpler types. We show that our algorithm is sound, complete and decidable with respect to a declarative formulation of subtyping based on the minimal relevant logic B + . Moreover, it leads to a simple and compact implementation in under 50 lines of functional code.

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Beltagy, I., Stephen Roller, Pengxiang Cheng, Katrin Erk, and Raymond J. Mooney. "Representing Meaning with a Combination of Logical and Distributional Models." Computational Linguistics 42, no. 4 (December 2016): 763–808. http://dx.doi.org/10.1162/coli_a_00266.

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NLP tasks differ in the semantic information they require, and at this time no single semantic representation fulfills all requirements. Logic-based representations characterize sentence structure, but do not capture the graded aspect of meaning. Distributional models give graded similarity ratings for words and phrases, but do not capture sentence structure in the same detail as logic-based approaches. It has therefore been argued that the two are complementary. We adopt a hybrid approach that combines logical and distributional semantics using probabilistic logic, specifically Markov Logic Networks. In this article, we focus on the three components of a practical system: 1 1) Logical representation focuses on representing the input problems in probabilistic logic; 2) knowledge base construction creates weighted inference rules by integrating distributional information with other sources; and 3) probabilistic inference involves solving the resulting MLN inference problems efficiently. To evaluate our approach, we use the task of textual entailment, which can utilize the strengths of both logic-based and distributional representations. In particular we focus on the SICK data set, where we achieve state-of-the-art results. We also release a lexical entailment data set of 10,213 rules extracted from the SICK data set, which is a valuable resource for evaluating lexical entailment systems. 2

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Garrett, Brian Jonathan. "Causal Essentialism versus the Zombie Worlds." Canadian Journal of Philosophy 39, no. 1 (March 2009): 93–112. http://dx.doi.org/10.1353/cjp.0.0042.

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David Chalmers claims that the logical possibility of ‘zombie worlds’ — worlds physically indiscernible from the actual world, but that lack consciousness — reveal that consciousness is a distinct fact, or property, in addition to the physical facts or properties.The ‘existence’ or possibility of Zombie worlds violates the physicalist demand that consciousness logically supervene upon the physical. On the assumption that the logical supervenience of consciousness upon the physical is, indeed, a necessary entailment of physicalism, the existence of zombie worlds implies the falsity of physicalism. How do we determine the logical possibility of zombie worlds? By conceptual analysis of the concepts involved, keeping empirical facts in mind.

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Borovcanin, Momcilo. "Some consequence relations on propositional formulas." Serbian Journal of Electrical Engineering 8, no. 1 (2011): 9–15. http://dx.doi.org/10.2298/sjee1101009b.

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Consequence relations on propositional formulas are binary relations on propositional formulas that represent certain types of entailment - formal or semi-formal derivation of conclusion from a certain set of premises. Some of well known examples are classical implication (standard logical entailment), preference relations (i.e. relations that satisfy Reflexivity, Left logical equivalence, Right weakening, And, Or and Cautious monotonicity) rational relations (i.e. preference relations that also satisfy rational monotonicity), consequence relations (prime examples are qualitative possibilities and necessities) etc. More than two decades various consequence relations are used in automated decision making, product control, risk assessment and so on. The aim of this paper is to give a short overview of the most prominent examples of consequence relations.

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Caminati, Marco. "First Order Languages: Further Syntax and Semantics." Formalized Mathematics 19, no. 3 (January 1, 2011): 179–92. http://dx.doi.org/10.2478/v10037-011-0027-0.

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First Order Languages: Further Syntax and SemanticsThird of a series of articles laying down the bases for classical first order model theory. Interpretation of a language in a universe set. Evaluation of a term in a universe. Truth evaluation of an atomic formula. Reassigning the value of a symbol in a given interpretation. Syntax and semantics of a non atomic formula are then defined concurrently (this point is explained in [16], 4.2.1). As a consequence, the evaluation of any w.f.f. string and the relation of logical implication are introduced. Depth of a formula. Definition of satisfaction and entailment (aka entailment or logical implication) relations, see [18] III.3.2 and III.4.1 respectively.

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Anisa, Febiyana. "THE TRUTH RELATIONS IN THE MAIN CHARACTER’S ENTAILMENT SENTENCES IN MURDER ON THE ORIENT EXPRESS MOVIE." MEDIOVA: Journal of Islamic Media Studies 1, no. 2 (November 29, 2021): 181–95. http://dx.doi.org/10.32923/medio.v1i2.1876.

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This study analyzed entailment of the main character’s sentences in Murder on The Orient Express movie in the semantics field. The purpose of this study is to explain the truth in the sentence uttered by the main character in the movie and to prove the truth value from the interlocutor’s response in the sentence. This study focused on explaining the truth of Poirot’s sentences and proving the truth value from the interlocutor’s response. This study used a qualitative descriptive method and a propositional logic approach. This study found 16 data of entailment. The data were analyzed using the theory of entailment from Fasold and Saeed, and theory of logic from Goranko and Hurley. The entailment sentences are entered into the truth table which explains the truth value of the sentence accompanied by logical explanations which are divided into deductive and inductive arguments. The truth value of the entailment sentence can be seen through the response of the main character's interlocutors.

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KASSOFF, MICHAEL, and MICHAEL R. GENESERETH. "PrediCalc: a logical spreadsheet management system." Knowledge Engineering Review 22, no. 3 (September 2007): 281–95. http://dx.doi.org/10.1017/s0269888907001154.

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AbstractIn this article, we describe PrediCalc, a logical spreadsheet that allows for many-to-many constraints and propagation in all directions. We explain PrediCalc’s update mechanism and PrediCalc’s unique approach to handling inconsistencies between the spreadsheet values and the spreadsheet formulas. We have developed a paraconsistent entailment relation for the purpose of computing the consequences of PrediCalc’s value assignments under inconsistency.We close with thoughts on the prospects of logical spreadsheets on the World Wide Web, and describe our initial Websheet prototypes.

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Rudolph, S., and B. Glimm. "Nominals, Inverses, Counting, and Conjunctive Queries or: Why Infinity is your Friend!" Journal of Artificial Intelligence Research 39 (October 28, 2010): 429–81. http://dx.doi.org/10.1613/jair.3029.

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Description Logics are knowledge representation formalisms that provide, for example, the logical underpinning of the W3C OWL standards. Conjunctive queries, the standard query language in databases, have recently gained significant attention as an expressive formalism for querying Description Logic knowledge bases. Several different techniques for deciding conjunctive query entailment are available for a wide range of DLs. Nevertheless, the combination of nominals, inverse roles, and number restrictions in OWL 1 and OWL 2 DL causes unsolvable problems for the techniques hitherto available. We tackle this problem and present a decidability result for entailment of unions of conjunctive queries in the DL ALCHOIQb that contains all three problematic constructors simultaneously. Provided that queries contain only simple roles, our result also shows decidability of entailment of (unions of) conjunctive queries in the logic that underpins OWL 1 DL and we believe that the presented results will pave the way for further progress towards conjunctive query entailment decision procedures for the Description Logics underlying the OWL standards.

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BESNARD, PHILIPPE. "A LOGICAL ANALYSIS OF RULE INCONSISTENCY." International Journal of Semantic Computing 05, no. 03 (September 2011): 271–80. http://dx.doi.org/10.1142/s1793351x11001250.

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Representing knowledge in a rule-based system takes place by means of "if…then…" statements. These are called production rules for the reason that new information is produced when the rule fires. The logic attached to rule-based systems is taken to be classical inasmuch as "if…then…" is encoded by material implication. However, it appears that the notion of triggering "if…then…" amounts to different logical definitions. The paper investigates the matter, with an emphasis upon consistency because reading "if… then…" statements as rules calls for a notion of rule consistency that does not conform with consistency in the classical sense. Natural deduction is used to explore entailment and equivalence among various formulations and properties.

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Kruszewski, German, Denis Paperno, and Marco Baroni. "Deriving Boolean structures from distributional vectors." Transactions of the Association for Computational Linguistics 3 (December 2015): 375–88. http://dx.doi.org/10.1162/tacl_a_00145.

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Corpus-based distributional semantic models capture degrees of semantic relatedness among the words of very large vocabularies, but have problems with logical phenomena such as entailment, that are instead elegantly handled by model-theoretic approaches, which, in turn, do not scale up. We combine the advantages of the two views by inducing a mapping from distributional vectors of words (or sentences) into a Boolean structure of the kind in which natural language terms are assumed to denote. We evaluate this Boolean Distributional Semantic Model (BDSM) on recognizing entailment between words and sentences. The method achieves results comparable to a state-of-the-art SVM, degrades more gracefully when less training data are available and displays interesting qualitative properties.

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Kupperman, Joel J. "A New Look at the Logic of the ‘Is’-‘Ought’ Relation." Philosophy 80, no. 3 (July 2005): 343–59. http://dx.doi.org/10.1017/s0031819105000331.

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In the 1950's some prominent philosophers suggested a logical relation weaker than entailment between primarily descriptive statements and ethical conclusions. The paper revisits this suggestion. It examines four ways in which ethical statemnts can be supported by descriptions and evaluations. This provides a similarity bteween some kinds of reason-giving in ethics and familiar cases of logical inference, making it plausible to speak of a logic. The similarity however is limited, and the strength in ethics of descriptive reasons is never precise and always somewhat contestable.

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Costa, Jorge Campos da, and Claudia Strey. "INFERENCES AND INTERFACES: VALIDITY AND RELEVANCE." Linguagem em (Dis)curso 14, no. 3 (December 2014): 577–94. http://dx.doi.org/10.1590/1982-4017-140308-0814.

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The Ancient Greeks, since the sophists' texts represented threats to legitimate reasoning anchored in the notion of truth, tried to examine the relationship among valid, informal and fallacious arguments. Aristotle distinguished mainly formal ways of abstractions from the daily practical uses, addressing the relationships between the logical forms and the interferences of content. This paper, motivated by this script of insights, investigates problems concerning logical operators, relations of sense, probability, entailment and their properties in natural language, constituted as inferences in the logical-cognitive-communicative interface. For that, foundations of classical-propositional-logic are brought closer together with the ones from semantics, pragmatics and an inspiring notion of relevance.

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Levine, Michael P. "The Deterministic and Ontological Implications of the Logical Entailment Analysis of Causation." Idealistic Studies 17, no. 1 (1987): 1–13. http://dx.doi.org/10.5840/idstudies19871717.

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Lance, Mark, and Philip Kremer. "The logical structure of linguistic commitment II: Systems of relevant commitment entailment." Journal of Philosophical Logic 25, no. 4 (August 1996): 425–49. http://dx.doi.org/10.1007/bf00249667.

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Karivets', Ihor. "Elements, Types and Consequences of Scientific Creativity. Foreword to the Ukrainian Translation of Jan Łukasiewicz’s article “Creativity in Science”." Humanitarian vision 6, no. 2 (November 25, 2020): 40–42. http://dx.doi.org/10.23939/shv2020.02.040.

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For the first time, the article “Creativity in Science” by Jan Łukasiewicz, a well-known representative of the Lviv-Warsaw School, logician and methodologist of science, was translated into Ukrainian. A well-known logician refutes the thesis that sciences exist only to reproduce facts and establish truths based on them. Sciences exist to meet the intellectual needs of man, which are manifested in his desire to understand. Reasoning is a creative act that includes demonstration, deduction, affirmation and understanding, as well as creation of hypotheses. Scientific creativity consists in the formulation of constructive judgments, which are combined into certain syntheses, which can be called theories. They become scientific only when there are combined with logical relations of entailment and inference.

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Harrison, Jonathan. "The Logical Function of ‘That’, or Truth, Propositions and Sentences." Philosophy 79, no. 1 (January 2004): 67–96. http://dx.doi.org/10.1017/s0031819104000063.

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(i) It is propositions, not sentences, that are true or false. It is true ‘Dogs bark’ does not make sense. It is true that dogs bark does. (ii) and (iii) Davidson wrong about ‘that’. (iv) The difference between ‘implies’ and ‘if ... then ...’. (v), (vi), (vii) and (viii) Russell, not Quine, right about the subject matter of logic. (ix) The objectual and substitutional interpretations of quantifiers compatible. (x), (xi), (xii), (xiii), (xiv), (xv) and (xvi) Implications for well-known theories of truth; truth correspondence. (xvii), (xviii) and (xix) and (xx) Implications for the principle of bivalence, the law of excluded middle, and the principle of non-contradiction. (xxi) Recapitulation. (xxii) ‘That’ and entailment. (xxiii) Propositions not entities, subsistent or otherwise.

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Hanke, Miroslav. "Jan Dullaert of Ghent on the Foundations of Propositional Logic." Vivarium 55, no. 4 (November 22, 2017): 273–306. http://dx.doi.org/10.1163/15685349-12341348.

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Abstract Jan Dullaert (1480-1513) was a direct student of John Mair and a teacher of Gaspar Lax, Juan de Celaya, and Juan Luis Vives. His commentary on Aristotle’s Peri Hermeneias addresses the foundations of propositional logic, including a detailed analysis of conditionals (following Paul of Venice’s Logica magna) and the semantics of logical connectives (conjunction, disjunction, and implication). Dullaert’s propositional logic is limited to the immediate implications of the semantics of these connectives, i.e., their introduction and elimination rules. In the same context, he discusses several alternative treatments of semantic paradoxes, paying most attention to the approaches derived from Martin Le Maistre (based on the idea that sentential meaning is closed under entailment) and John Mair (based on the idea that self-falsifying sentences are false).

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González, Luis. "Discrete Entailment-Based Linking and -EE Nouns in English." Research in Language 5 (December 18, 2007): 51–79. http://dx.doi.org/10.2478/v10015-007-0002-6.

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Barker (1998) argues that since the referent of an -ee noun can be an indirect object, a direct object, a prepositional object, or a subject, -ee nouns cannot be described as a syntactic natural class. Portero Muñoz (2003) concurs and offers a semantic analysis based on Logical Structure (LS) in the framework of Role and Reference Grammar (RRG). This article proposes that RRG’s macroroles (Actor and Undergoer) can be derived with two entailments and without any need for LS. Its analysis improves Portero Muñoz’s, presenting additional evidence that subjects that allow -ee noun formation are Undergoers. It also explains why most -ee nouns are direct objects in spite of the fact that the suffi Xoriginated as a referent for indirect objects. Finally, it offers an explanation for nouns like amputee, pluckee, twistee, benefactee, malefactee, biographee, catapultee, razee, standee, attendee.

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Mitra, Arindam, Peter Clark, Oyvind Tafjord, and Chitta Baral. "Declarative Question Answering over Knowledge Bases Containing Natural Language Text with Answer Set Programming." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 3003–10. http://dx.doi.org/10.1609/aaai.v33i01.33013003.

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While in recent years machine learning (ML) based approaches have been the popular approach in developing endto-end question answering systems, such systems often struggle when additional knowledge is needed to correctly answer the questions. Proposed alternatives involve translating the question and the natural language text to a logical representation and then use logical reasoning. However, this alternative falters when the size of the text gets bigger. To address this we propose an approach that does logical reasoning over premises written in natural language text. The proposed method uses recent features of Answer Set Programming (ASP) to call external NLP modules (which may be based on ML) which perform simple textual entailment. To test our approach we develop a corpus based on the life cycle questions and showed that Our system achieves up to 18% performance gain when compared to standard MCQ solvers.

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Lance, Mark Norris, and Philip Kremer. "The logical structure of linguistic commitment I: Four systems of non-relevant commitment entailment." Journal of Philosophical Logic 23, no. 4 (August 1994): 369–400. http://dx.doi.org/10.1007/bf01048687.

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Fandinno, Jorge, David Pearce, Concepción Vidal, and Stefan Woltran. "Comparing the Reasoning Capabilities of Equilibrium Theories and Answer Set Programs." Algorithms 15, no. 6 (June 8, 2022): 201. http://dx.doi.org/10.3390/a15060201.

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Answer Set Programming (ASP) is a well established logical approach in artificial intelligence that is widely used for knowledge representation and problem solving. Equilibrium logic extends answer set semantics to more general classes of programs and theories. When intertheory relations are studied in ASP, or in the more general form of equilibrium logic, they are usually understood in the form of comparisons of the answer sets or equilibrium models of theories or programs. This is the case for strong and uniform equivalence and their relativised and projective versions. However, there are many potential areas of application of ASP for which query answering is relevant and a comparison of programs in terms of what can be inferred from them may be important. We formulate and study some natural equivalence and entailment concepts for programs and theories that are couched in terms of inference and query answering. We show that, for the most part, these new intertheory relations coincide with their model-theoretic counterparts. We also extend some previous results on projective entailment for theories and for the new connective called ork.

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Kakas, Antonis. "Informalizing Formal Logic." Informal Logic 39, no. 2 (June 5, 2019): 169–204. http://dx.doi.org/10.22329/il.v39i2.5169.

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This paper presents a way in which formal logic can be understood and reformulated in terms of argumentation that can help us unify formal and informal reasoning. Classical deductive reasoning will be expressed entirely in terms of notions and concepts from argumentation so that formal logical entailment is equivalently captured via the arguments that win between those supporting concluding formulae and arguments supporting contradictory formulae. This allows us to go beyond Classical Logic and smoothly connect it with human reasoning, thus providing a uniform argumentation-based view of both informal and formal logic.

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Ciola, Graziana. "Marsilius of Inghen on the Definition of consequentia." Vivarium 56, no. 3-4 (October 15, 2018): 272–91. http://dx.doi.org/10.1163/15685349-12341359.

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Abstract This paper offers an analysis of Marsilius of Inghen’s definition of consequentia and of his treatment of logical validity as presented in the first book of his treatise on Consequentiae. Comparing Marsilius of Inghen’s, John Buridan’s, and Albert of Saxony’s theories, the author argues that Marsilius’ account is based on a conception of consequence as a relation of entailment among propositions rather than as a type of conditional sentence and, thus, moves the discussion away from the sentential level. Therefore, Marsilius’ theory represents an original and important contribution to fourteenth-century discussions on consequences.

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Ciardelli, Ivano. "Questions as information types." Synthese 195, no. 1 (September 30, 2016): 321–65. http://dx.doi.org/10.1007/s11229-016-1221-y.

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Abstract This paper argues that questions have an important role to to play in logic, both semantically and proof-theoretically. Semantically, we show that by generalizing the classical notion of entailment to questions, we can capture not only the standard relation of logical consequence, which holds between pieces of information, but also the relation of logical dependency, which holds between information types. Proof-theoretically, we show that questions may be used in inferences as placeholders for arbitrary information of a given type; by manipulating such placeholders, we may construct formal proofs of dependencies. Finally, we show that such proofs have a specific kind of constructive content: they do not just witness the existence of a certain dependency, but actually encode a method for transforming information of the types described by the assumptions into information of the type described by the conclusion.

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Burgess-Jackson, Keith. "What Independence Is." Review of European Studies 12, no. 3 (August 10, 2020): 50. http://dx.doi.org/10.5539/res.v12n3p50.

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Eighty years ago, in a short essay entitled “What Is Independence?,” Richard Robinson (1902-1996) made two errors that, to my knowledge, remain uncorrected. The errors are (1) claiming that entailment entails consistency (it does not) and (2) misstating the relation of subcontrariness. To make good on my claim that these are errors, I present and explain, in a more systematic way than Robinson does, nine distinct logical relations, one of which is independence. There are independent reasons for making these relations—as well as their relations to one another—better known to philosophers.

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Chi, Zeyu. "Essence, Propria and Essentialist Explanation." History of Philosophy & Logical Analysis 23, no. 2 (December 18, 2020): 338–61. http://dx.doi.org/10.30965/26664275-02302004.

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Abstract In this paper I propose a notion of propria inspired by Aristotle, on which propria are non-essential, necessary properties explained by the essence of a thing. My proposal differs from the characterization of propria by Kit Fine and Kathrin Koslicki: unlike Fine, the relation of explanation on my account can’t be assimilated to a notion of logical entailment. In disagreement with Koslicki, I suggest that the explanatory relation at issue needs not be necessary. My account of essence is conceptually parsimonious: it illuminates the contribution of essence to explanation without relying on obscure notions such as Aristotelian form or identity.

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Marocco, Paolo, and Roberto Gigliucci. "An Investigation about Entailment and Narrative by AI Techniques (Generative Models)." Communication, Society and Media 3, no. 4 (November 16, 2020): p61. http://dx.doi.org/10.22158/csm.v3n4p61.

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Many storytelling generation problems concern the difficulty to model the sequence of sentences. Language models are generally able to assign high scores to well-formed text, especially in the cases of short texts, failing when they try to simulate human textual inference. Although in some cases output text automatically generated sounds as bland, incoherent, repetitive and unrelated to the context, in other cases the process reveals capability to surprise the reader, avoiding to be boring/predictable, even if the generated text satisfies entailment task requirements. The lyric tradition often does not proceed towards a real logical inference, but takes into account alternatives like the unexpectedness, useful for predicting when a narrative story will be perceived as interesting. To achieve a best comprehension of narrative variety, we propose a novel measure based on two components: inference and unexpectedness, whose different weights can modify the opportunity for readers to have different experiences about the functionality of a generated story. We propose a supervised validation treatment, in order to compare the authorial original text, learned by the model, with the generated one.

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Jäger, Christoph. "Fischer’s Fate with Fatalism." European Journal for Philosophy of Religion 9, no. 4 (December 19, 2017): 25–38. http://dx.doi.org/10.24204/ejpr.v9i4.2027.

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John Martin Fischer’s core project in Our Fate (2016) is to develop and defend Pike-style arguments for theological incompatibilism, i. e., for the view that divine omniscience is incompatible with human free will. Against Ockhamist attacks on such arguments, Fischer maintains that divine forebeliefs constitute so-called hard facts about the times at which they occur, or at least facts with hard ‘kernel elements’. I reconstruct Fischer’s argument and outline its structural analogies with an argument for logical fatalism. I then point out some of the costs of Fischer’s reasoning that come into focus once we notice that the set of hard facts is closed under entailment.

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Fang, Liangda, Kewen Wang, Zhe Wang, and Ximing Wen. "Disjunctive Normal Form for Multi-Agent Modal Logics Based on Logical Separability." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 2817–26. http://dx.doi.org/10.1609/aaai.v33i01.33012817.

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Modal logics are primary formalisms for multi-agent systems but major reasoning tasks in such logics are intractable, which impedes applications of multi-agent modal logics such as automatic planning. One technique of tackling the intractability is to identify a fragment called a normal form of multiagent logics such that it is expressive but tractable for reasoning tasks such as entailment checking, bounded conjunction transformation and forgetting. For instance, DNF of propositional logic is tractable for these reasoning tasks. In this paper, we first introduce a notion of logical separability and then define a novel disjunctive normal form SDNF for the multiagent logic Kn, which overcomes some shortcomings of existing approaches. In particular, we show that every modal formula in Kn can be equivalently casted as a formula in SDNF, major reasoning tasks tractable in propositional DNF are also tractable in SDNF, and moreover, formulas in SDNF enjoy the property of logical separability. To demonstrate the usefulness of our approach, we apply SDNF in multi-agent epistemic planning. Finally, we extend these results to three more complex multi-agent logics Dn, K45n and KD45n.

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Feiman, Roman, Joshua K. Hartshorne, and David Barner. "Contrast and entailment: Abstract logical relations constrain how 2- and 3-year-old children interpret unknown numbers." Cognition 183 (February 2019): 192–207. http://dx.doi.org/10.1016/j.cognition.2018.11.005.

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Du, Jianfeng, Jeff Z. Pan, Sylvia Wang, Kunxun Qi, Yuming Shen, and Yu Deng. "Validation of Growing Knowledge Graphs by Abductive Text Evidences." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 2784–91. http://dx.doi.org/10.1609/aaai.v33i01.33012784.

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This paper proposes a validation mechanism for newly added triples in a growing knowledge graph. Given a logical theory, a knowledge graph, a text corpus, and a new triple to be validated, this mechanism computes a sorted list of explanations for the new triple to facilitate the validation of it, where an explanation, called an abductive text evidence, is a set of pairs of the form (triple, window) where appending the set of triples on the left to the knowledge graph enforces entailment of the new triple under the logical theory, while every sentence window on the right which is contained in the text corpus explains to some degree why the triple on the left is true. From the angle of practice, a special class of abductive text evidences called TEP-based abductive text evidence is proposed, which is constructed from explanation patterns seen before in the knowledge graph. Accordingly, a method for computing the complete set of TEP-based abductive text evidences is proposed. Moreover, a method for sorting abductive text evidences based on distantly supervised learning is proposed. To evaluate the proposed validation mechanism, four knowledge graphs with logical theories are constructed from the four great classical masterpieces of Chinese literature. Experimental results on these datasets demonstrate the efficiency and effectiveness of the proposed mechanism.

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Hanke, Miroslav. "Scholastická logika „vědění“ III." Studia Neoaristotelica 18, no. 3 (2021): 1–107. http://dx.doi.org/10.5840/studneoar202118310.

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The problem of logical omniscience breaks down to the problems of the closure of knowledge under implication and of the distribution of knowledge over implication. In late medieval scholasticism these two related issues were engaged in various genres, in particular in general analysis of validity, games of obligationes, solution to self-referential antinomies and semantics of terms. The present study analyses the corpus of fourteenth-century texts with some overreaches to the subsequent two centuries, attempting to cover representatives of both the “British” and the “Continental” tradition. With some degree of simplification, this results in a range of four basic positions: 1. knowledge is closed under “analytic entailment” (Buridan), 2. knowledge distributes over implication (Heytesbury), 3. knowledge distributes over implication provided that its consequent’s truth is being taken into consideration (Peter of Mantua), 4. knowledge does not distribute overimplication (Wyclif).

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Gimeno-Simó, Joan. "On how to legitimately constrain a semantic theory." Semiotica 2021, no. 240 (March 4, 2021): 97–127. http://dx.doi.org/10.1515/sem-2021-0014.

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Abstract Semanticists often restrict their theories by imposing constraints on the parameters that can be employed for interpreting the expressions of a language. Such constraints are based on non-logical features of actual contexts of utterance, but they often have important effects on issues that do pertain to logic, like analyticity or entailment. For example, Kaplan’s restriction to so-called “proper contexts” was required in order to count “I am here now” as valid. In this paper I argue that constraints of this kind are often posited in an arbitrary and non-consistent way, and that they yield the intended results only at the price of imposing ad hoc principles whose justification could in turn justify further, often undesirable restrictions into the theory. I also introduce a criterion for telling whether such constraints are imposed in a legitimate manner.

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Gardner, Philippa. "Equivalences between logics and their representing type theories." Mathematical Structures in Computer Science 5, no. 3 (September 1995): 323–49. http://dx.doi.org/10.1017/s0960129500000785.

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We propose a new framework for representing logics, called LF+, which is based on the Edinburgh Logical Framework. The new framework allows us to give, apparently for the first time, general definitions that capture how well a logic has been represented. These definitions are possible because we are able to distinguish in a generic way that part of the LF+ entailment corresponding to the underlying logic. This distinction does not seem to be possible with other frameworks. Using our definitions, we show that, for example, natural deduction first-order logic can be well-represented in LF+, whereas linear and relevant logics cannot. We also show that our syntactic definitions of representation have a simple formulation as indexed isomorphisms, which both confirms that our approach is a natural one and provides a link between type-theoretic and categorical approaches to frameworks.

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Sabharwal, Chaman L., and Jennifer L. Leopold. "Evolution of Region Connection Calculus to VRCC-3D+." New Mathematics and Natural Computation 10, no. 02 (June 3, 2014): 103–41. http://dx.doi.org/10.1142/s1793005714500069.

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Qualitative spatial reasoning (QSR) is useful for deriving logical inferences when quantitative spatial information is not available. QSR theories have applications in areas such as geographic information systems, spatial databases, robotics, and cognitive sciences. The existing QSR theories have been applied primarily to 2D. The ability to perform QSR over a collection of 3D objects is desirable in many problem domains. Here we present the evolution (VRCC-3D+) of RCC-based QSR from 2D to both 3D (including occlusion support) and 4D (a temporal component). It is time consuming to construct large composition tables manually. We give a divide-and-conquer algorithm to construct a comprehensive composition table from smaller constituent tables (which can be easily handcrafted). In addition to the logical consistency entailment checking that is required for such a system, clearly there is a need for a spatio-temporal component to account for spatial movements and path consistency (i.e. to consider only smooth transitions in spatial movements over time). Visually, these smooth movement phenomena are represented as a conceptual neighborhood graph. We believe that the methods presented herein to detect consistency, refine uncertainty, and enhance reasoning about 3D objects will provide useful guidelines for other studies in automated spatial reasoning.

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Terrone, Enrico. "Observers and Narrators in Fiction Film." Croatian journal of philosophy 22, no. 65 (September 15, 2022): 201–15. http://dx.doi.org/10.52685/cjp.22.65.4.

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In the debate on our engagement with and appreciation of fiction films, the thesis that the viewer of a fiction film imagines observing fictional events, and the thesis that these events are imagined to be presented by a narrator, are usually taken as two components of one theoretical package, which philosophers such as George Wilson and Jerrold Levison defend, while philosophers such as Gregory Currie and Berys Gaut reject. This paper argues that the two theses can be disentangled and investigates their logical connection. The investigation shows that the second thesis entails the first but there is no entailment the other way around. Endorsing the first thesis is thus compatible with two options, namely endorsing the second thesis or abandoning it. However, the paper argues that if we endorse the first thesis, endorsing the second provides us with a more compelling explanation of our engagement with and appreciation of fiction films.

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SULLIVAN, Jessica, Kathryn DAVIDSON, Shirlene WADE, and David BARNER. "Differentiating scalar implicature from exclusion inferences in language acquisition." Journal of Child Language 46, no. 04 (April 10, 2019): 733–59. http://dx.doi.org/10.1017/s0305000919000096.

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AbstractDuring acquisition, children must learn both the meanings of words and how to interpret them in context. For example, children must learn the logical semantics of the scalar quantifier some and its pragmatically enriched meaning: ‘some but not all’. Some studies have shown that ‘scalar implicature’ – that some implies ‘some but not all’ – poses a challenge even to nine-year-olds, while others find success by age three. We asked whether reports of children's successes might be due to the computation of exclusion inferences (like contrast or mutual exclusivity) rather than scalar implicatures. We found that young children (N = 214; ages 4;0–7;11) sometimes compute symmetrical exclusion inferences rather than asymmetric scalar inferences. These data suggest that a stronger burden of evidence is required in studies of implicature; before concluding that children compute implicatures, researchers should first show that children exhibit sensitivity to asymmetric entailment in the task.

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Liu, Hanmeng, Leyang Cui, Jian Liu, and Yue Zhang. "Natural Language Inference in Context - Investigating Contextual Reasoning over Long Texts." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 15 (May 18, 2021): 13388–96. http://dx.doi.org/10.1609/aaai.v35i15.17580.

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Natural language inference (NLI) is a fundamental NLP task, investigating the entailment relationship between two texts. Popular NLI datasets present the task at sentence-level. While adequate for testing semantic representations, they fall short for testing contextual reasoning over long texts, which is a natural part of the human inference process. We introduce ConTRoL, a new dataset for ConTextual Reasoning over Long texts. Consisting of 8,325 expert-designed "context-hypothesis" pairs with gold labels, ConTRoL is a passage-level NLI dataset with a focus on complex contextual reasoning types such as logical reasoning. It is derived from competitive selection and recruitment test (verbal reasoning test) for police recruitment, with expert level quality. Compared with previous NLI benchmarks, the materials in ConTRoL are much more challenging, involving a range of reasoning types. Empirical results show that state-of-the-art language models perform by far worse than educated humans. Our dataset can also serve as a testing-set for downstream tasks like checking the factual correctness of summaries.

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Zobl, Helmut. "A functional approach to the attainability of typological targets in L2 acquisition." Interlanguage studies bulletin (Utrecht) 2, no. 1 (June 1986): 16–32. http://dx.doi.org/10.1177/026765838600200102.

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This paper proposes a functional, parsing-based approach to the attainability of typological targets in L1 and L2 acquisition. Ideally, there should be a functional synchronization between the order in which principles constituting typological values emerge in learner grammars and the computational demands imposed by the simplest data instantiating a typological value. In L2 acquisition this functional synchronization is jeopardized by the possibility of L1-inspired misparses which may impute more structure to an input string than is consistent with a minimal parse. As a result, the more marked typological setting or the implicans of two grammatical principles in a relationship of logical entailment can appear first in interlanguage grammars. In L1 acquisition, on the other hand, misparses appear to be the result of assuming too little structure. Because of these differences, recovery from an inappropriate value follows different courses in L1 and L2 acquisition. It is proposed that this difference has important implications for the learn-ability of first and second languages.

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Bar-Haim, Roy, Ido Dagan, and Jonathan Berant. "Knowledge-Based Textual Inference via Parse-Tree Transformations." Journal of Artificial Intelligence Research 54 (September 9, 2015): 1–57. http://dx.doi.org/10.1613/jair.4584.

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Textual inference is an important component in many applications for understanding natural language. Classical approaches to textual inference rely on logical representations for meaning, which may be regarded as "external" to the natural language itself. However, practical applications usually adopt shallower lexical or lexical-syntactic representations, which correspond closely to language structure. In many cases, such approaches lack a principled meaning representation and inference framework. We describe an inference formalism that operates directly on language-based structures, particularly syntactic parse trees. New trees are generated by applying inference rules, which provide a unified representation for varying types of inferences. We use manual and automatic methods to generate these rules, which cover generic linguistic structures as well as specific lexical-based inferences. We also present a novel packed data-structure and a corresponding inference algorithm that allows efficient implementation of this formalism. We proved the correctness of the new algorithm and established its efficiency analytically and empirically. The utility of our approach was illustrated on two tasks: unsupervised relation extraction from a large corpus, and the Recognizing Textual Entailment (RTE) benchmarks.

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Jasbi, Masoud, Natalia Bermudez, and Kathryn Davidson. "Default biases in the interpretation of English negation, conjunction, and disjunction." Experiments in Linguistic Meaning 2 (January 27, 2023): 129. http://dx.doi.org/10.3765/elm.2.5382.

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Previous research has hypothesized default interpretive biases for three types of ambiguities with English logical words and, or, and not. First, disjunction (A or B) is hypothesized to be biased towards an exclusive interpretation in upward-entailing environments and an inclusive interpretation in downward-entailing environments (Levinson 2000, Chierchia 2004, Breheny et al. 2005). A negated disjunction (not A or B) is claimed to be biased towards a “neither-nor” interpretation (i.e. wide scope negation: ¬[A ∨ B]) and a negated conjunction is said to be biased towards an “either-not” interpretation (i.e. wide-scope negation: ¬[A ∧ B]) (Szabolcsi 2002, Szabolcsi & Haddican 2004). We tested these hypotheses within the same experimental paradigm with 149 English-speaking participants and found disjunction to be biased towards an inclusive interpretation across three different entailment environments: episodic declaratives, questions, and conditional antecedents. Our results also confirmed that English negated disjunction is biased towards a “neither-nor” (wide scope negation) interpretation but the results did not show an “either-not” bias (wide scope negation) for negated conjunction.

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Halldén, Sören. "A question concerning a logical calculus related to Lewis' System of strict implication, which is of special interest for the study of entailment." Theoria 14, no. 3 (February 11, 2008): 265–69. http://dx.doi.org/10.1111/j.1755-2567.1948.tb00896.x.

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Gabbay, Dov M., and Ruy J. G. B. de Queiroz. "Extending the Curry-Howard interpretation to linear, relevant and other resource logics." Journal of Symbolic Logic 57, no. 4 (December 1992): 1319–65. http://dx.doi.org/10.2307/2275370.

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The so-called Curry-Howard interpretation (Curry [1934], Curry and Feys [1958], Howard [1969], Tait [1965]) is known to provide a rather neat term-functional account of intuitionistic implication. Could one refine the interpretation to obtain an almost as good account of other neighbouring implications, including the so-called ‘resource’ implications (e.g. linear, relevant, etc.)?We answer this question positively by demonstrating that just by working with side conditions on the rule of assertability conditions for the connective representing implication (‘→’) one can characterise those ‘resource’ logics. The idea stems from the realisation that whereas the elimination rule for conditionals (of which implication is a particular case) remains virtually unchanged no matter what kind of conditional one has (i.e. linear, relevant, intuitionistic, classical, etc., all have modus ponens), the corresponding introduction rule carries an element of vagueness which can be explored in the characterisation of several sorts of conditionals. The rule of →-introduction is classified as an ‘improper’ inference rule, to use a terminology from Prawitz [1965]. Now, the so-called improper rules leave room for manoeuvre as to how a particular logic can be obtained just by imposing conditions on the discharge of assumptions that would correspond to the particular logical discipline one is adopting (linear, relevant, ticket entailment, intuitionistic, classical, etc.). The side conditions can be ‘naturally’ imposed, given that a degree of ‘vagueness’ is introduced by the presentation of those improper inference rules, such as the rule of →-introduction:which says: starting from assumption ‘A’, and arriving at ‘B’ via an unspecified number of steps, one can discharge the assumption and conclude that ‘A’ implies ‘B’.

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Journal articles on the topic 'Logical entailment'

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