Relevant bibliographies by topics / Logical entailment

Academic literature on the topic 'Logical entailment'

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Published: 10 December 2022
Last updated: 28 January 2023

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Journal articles on the topic "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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Dissertations / Theses on the topic "Logical entailment"

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Erickson, Evelyn Fernandes. "An investigation of logical pluralism and b-entailment." PROGRAMA DE P?S-GRADUA??O EM FILOSOFIA, 2016. https://repositorio.ufrn.br/jspui/handle/123456789/22409.

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O pluralismo l?gico vem recentemente chamando aten??o, com v?rios autores contestando sua natureza. O pluralismo l?gico ? a posi??o que diz que h? mais de uma l?gica correta ou leg?tima, o que pode ser articulado de diferentes maneiras. A presente disserta??o participa nesse debate explorando o framework do ?-entailment no contexto de variedades do pluralismo presentes na literatura. O ?-entailment ? uma no??o de consequ?ncia l?gica que ? capaz de expressar outras rela??es, como as l?gicas multi-dimensionais. Em particular, esse estudo examina quatro posi??es sobre o pluralismo: o pluralismo ecl?tico de Shapiro, o pluralismo atrav?s de GTT de Beall e Restall, o pluralismo intra-te?rico de Hjortland e os pluralismos atrav?s de teoria das demonsta??es de Restall e Paoli. Ser? mostrado como o ?-entailment se encaixa nessas variedades de pluralismo e tamb?m como fica em falta em certos aspectos. O objetivo da disserta??o ? tanto contribuir para a discuss?o sobre o pluralismo l?gico quanto expandir a discuss?o sobre o ?-entailment e outras no??es de consequ?ncia l?gica desse g?nero.
Logical pluralism has recently been given much attention, with numerous authors contesting its nature. In a broad sense, logical pluralism is the view that there are more than one correct or legitimate logic, which can be articulated in different ways. The present study participates in this debate by exploring the framework of ?-entailment in the context of several of varieties of pluralism. ?-entailment is a logical consequence relation, which may express different consequence relations, such as those of many-dimensional logics. In particular, this study examines four different takes on pluralism: Shapiros?s eclectic pluralism, Beall and Restall?s GTT pluralism, Hjortland?s intra-theoretic pluralism and Restall and Paoli?s pluralism based on proof-theory. It will be shown how ?-entailment fits into these varieties of pluralism, and a discussion is presented on how ?-entailment falls short is some aspects. The aim is to contribute to the discussion on logical pluralism as well as to expand the discussion about ?-entailment and consequence relations of this sort.
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Fjellstad, Andreas. "Transparency, transitivity or reflexivity." Thesis, University of Aberdeen, 2015. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=228553.

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This thesis investigates logico-philosophical aspects of using either a non-transitive or a non-reflexive logic to obtain a logic of truth in which truth is transparent. It enquires into and rejects the claim that restricting transitivity of entailment to accommodate transparent truth suffices to make the connective tonk acceptable by arguing that tonk as defined in a cut-free sequent calculus requires in addition that the logic is non-reflexive to be uniquely defined, and develops a semantics for tonk based on models with two valuations which delivers a non-transitive and non-reflexive logic. It develops a cut-free sequent calculus and two kinds of semantics for a non-reflexive logic of truth in which truth is transparent, one based on trivalent models and one based on models with two valuations. It shows how to define a non-transitive, a paraconsistent and a paracomplete logic of truth on the models with two valuations and develops a cut-free sequent calculus that captures all four logics. It investigates to which extent the non-reflexive and the non-transitive logic of truth can express their own meta-inferences, and shows among other things how one can employ the paraconsistent and the paracomplete logic to express the meta-inferences of the non-transitive and the non-reflexive logic respectively. Finally, it proves that the non-transitive logic of truth is omega-inconsistent and furthermore that transitivity is not required as assumption to establish that a logic in which truth satisfies the conditions of quantified standard deontic logic is omega-inconsistent.
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Dickson, Mark Lloyd. "Irreducible complexity as a nexus for an interdisciplinary dialogue between machine logic, molecular biology and theology / by M.L. Dickson." Thesis, North-West University, 2007. http://hdl.handle.net/10394/740.

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The claim that a principle known as Irreducible Complexity (IC) is empirically discoverable is investigated successively from the perspective of engineering, then molecular biology and finally theology, with the aim of evaluating the utility of IC for an interdisciplinary dialogue between all three. In the process, IC is subjected to the principle objections presented against it in the literature, leading to the conclusion that IC is sufficiently resistant to scientific criticism to be accepted as a true property of certain living systems. The ubiquity of machine descriptors in the professional literature of molecular biology is scrutinised in the context of the role of metaphor in science, as well as in the context of entailment models. A Biblical Theological approach to the Bible is harnessed to establish a framework for estimating the extent to which the story of Christ warrants expectation of first order design formalisms in nature, and whether that story within itself provides any homomorphic exemplification of IC. Additionally, key theological criticisms of IC are evaluated as well as criticisms of the Neo Darwinian revisioning of the Biblical account. The overall conclusion is that a true interdisciplinary dialogue where IC is the nexus holds theoretical as well as experimental promise.
Thesis (M.A. (Dogmatics))--North-West University, Potchefstroom Campus, 2008.
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Van, der Vyver Thelma. "Proof systems for propositional modal logic." Diss., 1997. http://hdl.handle.net/10500/16280.

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In classical propositional logic (CPL) logical reasoning is formalised as logical entailment and can be computed by means of tableau and resolution proof procedures. Unfortunately CPL is not expressive enough and using first order logic (FOL) does not solve the problem either since proof procedures for these logics are not decidable. Modal propositional logics (MPL) on the other hand are both decidable and more expressive than CPL. It therefore seems reasonable to apply tableau and resolution proof systems to MPL in order to compute logical entailment in MPL. Although some of the principles in CPL are present in MPL, there are complexities in MPL that are not present in CPL. Tableau and resolution proof systems which address these issues and others will be surveyed here. In particular the work of Abadi & Manna (1986), Chan (1987), del Cerro & Herzig (1988), Fitting (1983, 1990) and Gore (1995) will be reviewed.
Computing
M. Sc. (Computer Science)
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Siblini, Reda. "Recognizing Textual Entailment Using Description Logic And Semantic Relatedness." Thesis, 2014. http://spectrum.library.concordia.ca/978489/1/Siblini_PhD_S2014.pdf.

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Textual entailment (TE) is a relation that holds between two pieces of text where one reading the first piece can conclude that the second is most likely true. Accurate approaches for textual entailment can be beneficial to various natural language processing (NLP) applications such as: question answering, information extraction, summarization, and even machine translation. For this reason, research on textual entailment has attracted a significant amount of attention in recent years. A robust logical-based meaning representation of text is very hard to build, therefore the majority of textual entailment approaches rely on syntactic methods or shallow semantic alternatives. In addition, approaches that do use a logical-based meaning representation, require a large knowledge base of axioms and inference rules that are rarely available. The goal of this thesis is to design an efficient description logic based approach for recognizing textual entailment that uses semantic relatedness information as an alternative to large knowledge base of axioms and inference rules. In this thesis, we propose a description logic and semantic relatedness approach to textual entailment, where the type of semantic relatedness axioms employed in aligning the description logic representations are used as indicators of textual entailment. In our approach, the text and the hypothesis are first represented in description logic. The representations are enriched with additional semantic knowledge acquired by using the web as a corpus. The hypothesis is then merged into the text representation by learning semantic relatedness axioms on demand and a reasoner is then used to reason over the aligned representation. Finally, the types of axioms employed by the reasoner are used to learn if the text entails the hypothesis or not. To validate our approach we have implemented an RTE system named AORTE, and evaluated its performance on recognizing textual entailment using the fourth recognizing textual entailment challenge. Our approach achieved an accuracy of 68.8 on the two way task and 61.6 on the three way task which ranked the approach as 2nd when compared to the other participating runs in the same challenge. These results show that our description logical based approach can effectively be used to recognize textual entailment.
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Chang, Fu-Chieh, and 張富傑. "A Formal Logic Approach to Chinese Recognizing Textual Entailment." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/68400557821193296503.

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碩士
國立臺灣大學
電子工程學研究所
102
In the research of natural language processing (NLP), understanding the natural language is always a challenging problem. Traditionally, the research of NLP focuses on the semantics and logic of natural language. However, the present NLP research trend is focusing on the big data and machine learning techniques. These two methods have their own pros and cons; however, the traditional research of semantics and logic are seldom discussed in the recent works, and the existing machine learning techniques also have their limitations. Combining the traditional works on semantics with machine learning techniques is a good perspective to research. We build a system to solve the Chinese recognizing textual entailment (RTE) problem by formal logic method. Based on the theory of formal semantics and computational semantics, first, we use the machine learning technique to convert Chinese sentences in natural language into syntax trees. Then, we propose an algorithm to convert the syntax trees into semantic representations. Also, we propose a method that solves the RTE problem by integrating external knowledge resources with the proposed semantic representations. With these semantic representations, we can use the theorem proving techniques to solve the problem of Chinese RTE. Then, we demonstrate that our approach can solve some simple cases of Chinese RTE. Also, we show the possibilities and difficulties to solve the real-world cases. Finally, we point out the strengths and weaknesses of our system, and the possibilities on future research to improve our system.
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McQueen, Kelvin James. "A priori entailment and the metaphysics of science." Phd thesis, 2013. http://hdl.handle.net/1885/155983.

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In this dissertation I develop a framework for evaluating theories of fundamental reality and a related framework for evaluating reductive explanations. The former is the A Priori Entailment thesis (AET), which states that all truths are a priori deducible from the fundamental truths. The latter is the Reduction Entailment thesis (RET), which states that a successful and complete reductive explanation requires that the explanandum is a priori deducible from the explanans. After defending AET/RET I use them to resolve disputes in quantum metaphysics. The dissertation is split into four chapters. The first chapter evaluating the A Priori Entailment Thesis motivates underlying semantic and epistemological theses. It then defines a procedure for evaluating AET: a priori entailment expansions. These formulate problem cases into complex conditionals (of the form 'If [fundamental truths] then [non-fundamental truths]') and breaks them down into a number of simpler conditionals whose epistemic statuses are easier to evaluate. A priori entailment expansions are structured to guarantee that if the expansion conditionals are a priori then the expanded conditional is too. Chapter two A Priori Entailment as a Constraint on Classical Physical Theories constructs a number of entailment expansions showing that AET is true of worlds described by classical physics. Each expansion conditional in each entailment expansion is a case study in itself, with the potential to support or undermine AET. The primary case study shows that mass additivity is an a priori consequence of Newton's fundamental laws. I go on to argue that a particular metaphysical thesis explains these results. This metaphysical thesis strongly suggests that AET holds for any adequate fundamental theory, so AET must be true of the actual world. Chapter three Evaluating the Reduction Entailment Thesis defends RET. I compare the mass additivity expansion to the scientific explanation of mass additivity in physics. I show that the expansion can be seen as the result of removing subtle simplification-induced explanatory gaps exhibited by the scientific explanation. I use this to argue that a priori entailment is necessary for reductive explanation, as it is necessary for the explanatory gaps to be innocuous. I develop a method for systematically converting any reductive explanation into an a priori entailment expansion. I extend the account to inhomogeneous reductive explanations. I then relate RET to the reduction of consciousness and the mind-body problem. The final chapter A Priori Entailment as a Constraint on Quantum Theories assumes AET/RET and is the first detailed attempt at apply AET/RET to solutions to the quantum measurement problem. Such solutions are criticised for failing to reductively explain the manifest world. I evaluate such claims in the context of dynamical collapse theories. I object to the idea that such theories cannot explain why the manifest world appears three-dimensional. However, I provide new reasons for thinking that such theories cannot explain the existence of ordinary objects. In particular, I use AET/RET to show that dynamical collapse theories are empirically false.
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Books on the topic "Logical entailment"

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Zhi yue luo ji: Chuan tong luo ji yu xian dai luo ji di jie he. Guiyang Shi: Guizhou ren min chu ban she, 1985.

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Burchardt, Aljoscha. Modeling textual entailment with role-semantic information. Saarbrücken: German Research Center for Artifical Intelligence, 2008.

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1930-, Belnap Nuel D., and Dunn J. Michael 1941-, eds. Entailment: The logic of relevance and necessity. 2nd ed. Princeton, N.J: Princeton University Press, 1990.

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Sidorenko, E. A. Relevantnai︠a︡ logika: Predposylki, ischislenii︠a︡, semantika. Moskva: IFRAN, 2000.

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Patterson, Richard. Aristotle's modal logic: Essence and entailment in the Organon. Cambridge: Cambridge University Press, 1995.

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Zaĭt︠s︡ev, D. V. Obobshchennai︠a︡ relevantnai︠a︡ logika i modeli rassuzhdeniĭ: Monografii︠a︡. Moskva: Kreativnai︠a︡ ėkonomika, 2010.

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Burgess, John P. No Requirement of Relevance. Edited by Stewart Shapiro. Oxford University Press, 2009. http://dx.doi.org/10.1093/oxfordhb/9780195325928.003.0024.

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Classic logic defines entailment to hold between a premise (or set of premises) and a conclusion if and only if their logical form guarantees that either the premise (or at least one element of the set of premises) is false, or the conclusion is true. The definition obliges the logician to recognize certain degenerate entailments. A premise (or set of premises) that is contradictory in the sense that its logical form guarantees that it is false (or that at least one element of the set of is false) entails any conclusion: ex falso quodlibet. And a conclusion that is tautologous in the sense that its logical form guarantees that it is true is entailed by any premise (or set of premises): ex quolibet verum. The commitment of classical logic to these principles has frequently been attacked by indignant critics who denounce the degenerate cases of entailment as “paradoxes.”
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Belnap, Nuel D., J. Michael Dunn, and Alan Ross Anderson. Entailment. Princeton Univ Pr, 1992.

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Holliday, Wesley H., and Thomas F. III Icard. Axiomatization in the Meaning Sciences. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198739548.003.0002.

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While much of semantic theorizing is based on intuitions about logical phenomena associated with linguistic constructions—phenomena such as consistency and entailment—it is rare to see axiomatic treatments of linguistic fragments. Given a fragment interpreted in some class of formally specified models, it is often possible to ask for a characterization of the reasoning patterns validated by the class of models. Axiomatizations provide such a characterization, often in a perspicuous and efficient manner. This chapter highlights some of the benefits of providing axiomatizations for the purpose of semantic theorizing. Three examples from the study of modality provide an illustration of these benefits.
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Crupi, Vincenzo, and Katya Tentori. Confirmation Theory. Edited by Alan Hájek and Christopher Hitchcock. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780199607617.013.33.

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We first discuss several qualitative properties of confirmation as analyzed in a probabilistic framework. Some of these properties are classical, while others are relatively novel; some are shared by absolute and incremental confirmation, others are distinctive for each kind. We then proceed to address axiomatic characterizations of major classes of probabilistic measures of incremental confirmation. This treatment includes an original result displaying how conditions which single out the traditional probability difference measure up to ordinal equivalence. Finally, we argue that the longstanding project of a compelling confirmation-theoretic generalization of logical entailment (and refutation) can be achieved, provided that the right explicatum is adopted (to wit, a relative distance measure). This conclusion, we submit, dispels concerns that have been aired in the literature up to recent times.
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Book chapters on the topic "Logical entailment"

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Bos, Johan, and Katja Markert. "Recognising Textual Entailment with Robust Logical Inference." In Machine Learning Challenges. Evaluating Predictive Uncertainty, Visual Object Classification, and Recognising Tectual Entailment, 404–26. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11736790_23.

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Levine, Michael P. "Miracles and the Logical Entailment Analysis of Causation." In Hume and the Problem of Miracles: A Solution, 53–64. Dordrecht: Springer Netherlands, 1989. http://dx.doi.org/10.1007/978-94-009-2245-7_5.

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Bochman, Alexander. "Prolegomena to a Theory of Defeasible Entailment." In A Logical Theory of Nonmonotonic Inference and Belief Change, 213–50. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-662-04560-2_8.

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Alrabbaa, Christian, Franz Baader, Stefan Borgwardt, Raimund Dachselt, Patrick Koopmann, and Julián Méndez. "Evonne: Interactive Proof Visualization for Description Logics (System Description)." In Automated Reasoning, 271–80. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-10769-6_16.

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AbstractExplanations for description logic (DL) entailments provide important support for the maintenance of large ontologies. The “justifications” usually employed for this purpose in ontology editors pinpoint the parts of the ontology responsible for a given entailment. Proofs for entailments make the intermediate reasoning steps explicit, and thus explain how a consequence can actually be derived. We present an interactive system for exploring description logic proofs, called Evonne, which visualizes proofs of consequences for ontologies written in expressive DLs. We describe the methods used for computing those proofs, together with a feature called signature-based proof condensation. Moreover, we evaluate the quality of generated proofs using real ontologies.
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Echenim, Mnacho, Radu Iosif, and Nicolas Peltier. "Unifying Decidable Entailments in Separation Logic with Inductive Definitions." In Automated Deduction – CADE 28, 183–99. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-79876-5_11.

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AbstractThe entailment problem $$\upvarphi \models \uppsi $$ φ ⊧ ψ in Separation Logic [12, 15], between separated conjunctions of equational ($$x \approx y$$ x ≈ y and $$x \not \approx y$$ x ≉ y ), spatial ($$x \mapsto (y_1,\ldots ,y_\upkappa )$$ x ↦ ( y 1 , … , y κ ) ) and predicate ($$p(x_1,\ldots ,x_n)$$ p ( x 1 , … , x n ) ) atoms, interpreted by a finite set of inductive rules, is undecidable in general. Certain restrictions on the set of inductive definitions lead to decidable classes of entailment problems. Currently, there are two such decidable classes, based on two restrictions, called establishment [10, 13, 14] and restrictedness [8], respectively. Both classes are shown to be in $$\mathsf {2\text {EXPTIME}}$$ 2 EXPTIME by the independent proofs from [14] and [8], respectively, and a many-one reduction of established to restricted entailment problems has been given [8]. In this paper, we strictly generalize the restricted class, by distinguishing the conditions that apply only to the left- ($$\upvarphi $$ φ ) and the right- ($$\uppsi $$ ψ ) hand side of entailments, respectively. We provide a many-one reduction of this generalized class, called safe, to the established class. Together with the reduction of established to restricted entailment problems, this new reduction closes the loop and shows that the three classes of entailment problems (respectively established, restricted and safe) form a single, unified, $$\mathsf {2\text {EXPTIME}}$$ 2 EXPTIME -complete class.
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Bozga, Marius, Lucas Bueri, and Radu Iosif. "Decision Problems in a Logic for Reasoning About Reconfigurable Distributed Systems." In Automated Reasoning, 691–711. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-10769-6_40.

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AbstractWe consider a logic used to describe sets of configurations of distributed systems, whose network topologies can be changed at runtime, by reconfiguration programs. The logic uses inductive definitions to describe networks with an unbounded number of components and interactions, written using a multiplicative conjunction, reminiscent of Bunched Implications [37] and Separation Logic [39]. We study the complexity of the satisfiability and entailment problems for the configuration logic under consideration. Additionally, we consider the robustness property of degree boundedness (is every component involved in a bounded number of interactions?), an ingredient for decidability of entailments.
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Belnap, Nuel D. "Which Entailments Entail which Entailments?" In Directions in Relevant Logic, 185–96. Dordrecht: Springer Netherlands, 1989. http://dx.doi.org/10.1007/978-94-009-1005-8_14.

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Muggleton, Stephen. "Completing Inverse Entailment." In Inductive Logic Programming, 245–49. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/bfb0027328.

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Coquand, Thierry, Henri Lombardi, and Stefan Neuwirth. "Regular Entailment Relations." In Paul Lorenzen -- Mathematician and Logician, 103–14. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-65824-3_7.

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Abstract Inspired by the work of Lorenzen on the theory of preordered groups in the forties and fifties, we define regular entailment relations and show a crucial theorem for this structure. We also describe equivariant systems of ideals à la Lorenzen and show that the remarkable regularisation process he invented yields a regular entailment relation. By providing constructive objects and arguments, we pursue Lorenzen’s aim of “bringing to light the basic, pure concepts in their simple and transparent clarity”.
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Ciardelli, Ivano. "Dependency as Question Entailment." In Dependence Logic, 129–81. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-31803-5_8.

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Conference papers on the topic "Logical entailment"

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Bos, Johan, and Katja Markert. "Recognising textual entailment with logical inference." In the conference. Morristown, NJ, USA: Association for Computational Linguistics, 2005. http://dx.doi.org/10.3115/1220575.1220654.

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Arieli, Ofer, AnneMarie Borg, and Christian Straßer. "Characterizations and Classifications of Argumentative Entailments." In 18th International Conference on Principles of Knowledge Representation and Reasoning {KR-2021}. California: International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/kr.2021/6.

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In this paper we provide a detailed analysis of the inference process induced by logical argumentation frameworks. The frameworks may be defined with respect to any propositional language and logic, different arguments that represent deductions in the logic, various support-based attack relations between arguments, and all the complete Dung-style semantics for the frameworks. We show that, ultimately, for characterizing the inference process with respect to a given framework, extension-based semantics may be divided into two types: single-extension and multiple-extension, which induce respective kinds of entailment relations. These entailments are further classified by the way they tolerate new information (nonmonotonicity-related properties) and maintain conflicts among arguments (inconsistency-related properties).
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Suzuki, Riko, Hitomi Yanaka, Masashi Yoshikawa, Koji Mineshima, and Daisuke Bekki. "Multimodal Logical Inference System for Visual-Textual Entailment." In Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics: Student Research Workshop. Stroudsburg, PA, USA: Association for Computational Linguistics, 2019. http://dx.doi.org/10.18653/v1/p19-2054.

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Roth, Dan, and Mark Sammons. "Semantic and logical inference model for textual entailment." In the ACL-PASCAL Workshop. Morristown, NJ, USA: Association for Computational Linguistics, 2007. http://dx.doi.org/10.3115/1654536.1654558.

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Schwering, Christoph. "A Reasoning System for a First-Order Logic of Limited Belief." In Twenty-Sixth International Joint Conference on Artificial Intelligence. California: International Joint Conferences on Artificial Intelligence Organization, 2017. http://dx.doi.org/10.24963/ijcai.2017/173.

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Logics of limited belief aim at enabling computationally feasible reasoning in highly expressive representation languages. These languages are often dialects of first-order logic with a weaker form of logical entailment that keeps reasoning decidable or even tractable. While a number of such logics have been proposed in the past, they tend to remain for theoretical analysis only and their practical relevance is very limited. In this paper, we aim to go beyond the theory. Building on earlier work by Liu, Lakemeyer, and Levesque, we develop a logic of limited belief that is highly expressive but remains decidable in the first-order and tractable in the propositional case and exhibits some characteristics that make it attractive for an implementation. We introduce a reasoning system that employs this logic as representation language and present experimental results that showcase the benefit of limited belief.
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Ceylan, İsmail İlkan, Thomas Lukasiewicz, Enrico Malizia, and Andrius Vaicenavičius. "Explanations for Query Answers under Existential Rules." In Twenty-Eighth International Joint Conference on Artificial Intelligence {IJCAI-19}. California: International Joint Conferences on Artificial Intelligence Organization, 2019. http://dx.doi.org/10.24963/ijcai.2019/227.

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Ontology-mediated query answering is an extensively studied paradigm, which aims at improving query answers with the use of a logical theory. As a form of logical entailment, ontology-mediated query answering is fully interpretable, which makes it possible to derive explanations for query answers. Surprisingly, however, explaining answers for ontology-mediated queries has received little attention for ontology languages based on existential rules. In this paper, we close this gap, and study the problem of explaining query answers in terms of minimal subsets of database facts. We provide a thorough complexity analysis for several decision problems associated with minimal explanations under existential rules.
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Kaminski, Mark, Bernardo Cuenca Grau, Egor V. Kostylev, Boris Motik, and Ian Horrocks. "Stratified Negation in Limit Datalog Programs." In Twenty-Seventh International Joint Conference on Artificial Intelligence {IJCAI-18}. California: International Joint Conferences on Artificial Intelligence Organization, 2018. http://dx.doi.org/10.24963/ijcai.2018/259.

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There has recently been an increasing interest in declarative data analysis, where analytic tasks are specified using a logical language, and their implementation and optimisation are delegated to a general-purpose query engine. Existing declarative languages for data analysis can be formalised as variants of logic programming equipped with arithmetic function symbols and/or aggregation, and are typically undecidable. In prior work, the language of limit programs was proposed, which is sufficiently powerful to capture many analysis tasks and has decidable entailment problem. Rules in this language, however, do not allow for negation. In this paper, we study an extension of limit programs with stratified negation-as-failure. We show that the additional expressive power makes reasoning computationally more demanding, and provide tight data complexity bounds. We also identify a fragment with tractable data complexity and sufficient expressivity to capture many relevant tasks.
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Bednarczyk, Bartosz, and Sebastian Rudolph. "Worst-Case Optimal Querying of Very Expressive Description Logics with Path Expressions and Succinct Counting." In Twenty-Eighth International Joint Conference on Artificial Intelligence {IJCAI-19}. California: International Joint Conferences on Artificial Intelligence Organization, 2019. http://dx.doi.org/10.24963/ijcai.2019/212.

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Among the most expressive knowledge representation formalisms are the description logics of the Z family. For well-behaved fragments of ZOIQ, entailment of positive two-way regular path queries is well known to be 2EXPTIME-complete under the proviso of unary encoding of numbers in cardinality constraints. We show that this assumption can be dropped without an increase in complexity and EXPTIME-completeness can be achieved when bounding the number of query atoms, using a novel reduction from query entailment to knowledge base satisfiability. These findings allow to strengthen other results regarding query entailment and query containment problems in very expressive description logics. Our results also carry over to GC2, the two-variable guarded fragment of first-order logic with counting quantifiers, for which hitherto only conjunctive query entailment has been investigated.
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Gogacz, Tomasz, Víctor Gutiérrez-Basulto, Albert Gutowski, Yazmín Ibáñez-García, and Filip Murlak. "On Finite Entailment of Non-Local Queries in Description Logics." In 17th International Conference on Principles of Knowledge Representation and Reasoning {KR-2020}. California: International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/kr.2020/43.

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We study the problem of finite entailment of ontology-mediated queries. Going beyond local queries, we allow transitive closure over roles. We focus on ontologies formulated in the description logics ALCOI and ALCOQ, extended with transitive closure. For both logics, we show 2EXPTIME upper bounds for finite entailment of unions of conjunctive queries with transitive closure. We also provide a matching lower bound by showing that finite entailment of conjunctive queries with transitive closure in ALC is 2EXPTIME-hard
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Gogacz, Tomasz, Víctor Gutiérrez-Basulto, Yazmín Ibáñez-García, Jean Christoph Jung, and Filip Murlak. "On Finite and Unrestricted Query Entailment beyond SQ with Number Restrictions on Transitive Roles." In Twenty-Eighth International Joint Conference on Artificial Intelligence {IJCAI-19}. California: International Joint Conferences on Artificial Intelligence Organization, 2019. http://dx.doi.org/10.24963/ijcai.2019/238.

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We study the description logic SQ with number restrictions applicable to transitive roles, extended with either nominals or inverse roles. We show tight 2EXPTIME upper bounds for unrestricted entailment of regular path queries for both extensions and finite entailment of positive existential queries for nominals. For inverses, we establish 2EXPTIME-completeness for unrestricted and finite entailment of instance queries (the latter under restriction to a single, transitive role).
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Reports on the topic "Logical entailment"

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Bamber, D. A Characterization of Probabilistic Entailment in Adams' Logic of Conditionals. Fort Belvoir, VA: Defense Technical Information Center, September 1995. http://dx.doi.org/10.21236/ada301476.

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Koopmann, Patrick. Actions with Conjunctive Queries: Projection, Conflict Detection and Verification. Technische Universität Dresden, 2018. http://dx.doi.org/10.25368/2022.243.

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Description Logic actions specify adaptations of description logic interpretations based on some preconditions defined using a description logic. We consider DL actions in which preconditions can be specified using DL axioms as well as using conjunctive queries, and combinatiosn thereof. We investigate complexity bounds for the executability and the projection problem for these actions, which respectively ask whether an action can be executed on models of an interpretation, and which entailments are satisfied after an action has been executed on this model. In addition, we consider a set of new reasoning tasks concerned with conflicts and interactions that may arise if two action are executed at the same time. Since these problems have not been investigated before for Description Logic actions, we investigate the complexity of these tasks both for actions with conjunctive queries and without those. Finally, we consider the verification problem for Golog programs formulated over our famility of actions. Our complexity analysis considers several expressive DLs, and we provide tight complexity bounds for those for which the exact complexity of conjunctive query entailment is known.
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Borgwardt, Stefan, and Veronika Thost. Temporal Query Answering in DL-Lite with Negation. Technische Universität Dresden, 2015. http://dx.doi.org/10.25368/2022.221.

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Ontology-based query answering augments classical query answering in databases by adopting the open-world assumption and by including domain knowledge provided by an ontology. We investigate temporal query answering w.r.t. ontologies formulated in DL-Lite, a family of description logics that captures the conceptual features of relational databases and was tailored for efficient query answering. We consider a recently proposed temporal query language that combines conjunctive queries with the operators of propositional linear temporal logic (LTL). In particular, we consider negation in the ontology and query language, and study both data and combined complexity of query entailment.
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Koopmann, Patrick, and Jieying Chen. Deductive Module Extraction for Expressive Description Logics (Extended Version). Technische Universität Dresden, 2020. http://dx.doi.org/10.25368/2022.262.

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In deductive module extraction, we determine a small subset of an ontology for a given vocabulary that preserves all logical entailments that can be expressed in that vocabulary. While in the literature stronger module notions have been discussed, we argue that for applications in ontology analysis and ontology reuse, deductive modules, which are decidable and potentially smaller, are often sufficient. We present methods based on uniform interpolation for extracting different variants of deductive modules, satisfying properties such as completeness, minimality and robustness under replacements, the latter being particularly relevant for ontology reuse. An evaluation of our implementation shows that the modules computed by our method are often significantly smaller than those computed by existing methods.
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Baader, Franz, Stefan Borgwardt, and Marcel Lippmann. Temporal Conjunctive Queries in Expressive DLs with Non-simple Roles. Technische Universität Dresden, 2015. http://dx.doi.org/10.25368/2022.222.

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In Ontology-Based Data Access (OBDA), user queries are evaluated over a set of facts under the open world assumption, while taking into account background knowledge given in the form of a Description Logic (DL) ontology. Motivated by situation awareness applications, temporal conjunctive queries (TCQs) have recently been proposed as a useful extension of traditional OBDA to support the processing of temporal information. This paper extends the existing complexity analysis of TCQ entailment to very expressive DLs underlying the OWL 2 standard, and in contrast to previous work also allows for queries containing transitive roles.
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Baader, Franz, Stefan Borgwardt, and Marcel Lippmann. On the Complexity of Temporal Query Answering. Technische Universität Dresden, 2013. http://dx.doi.org/10.25368/2022.191.

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Ontology-based data access (OBDA) generalizes query answering in databases towards deduction since (i) the fact base is not assumed to contain complete knowledge (i.e., there is no closed world assumption), and (ii) the interpretation of the predicates occurring in the queries is constrained by axioms of an ontology. OBDA has been investigated in detail for the case where the ontology is expressed by an appropriate Description Logic (DL) and the queries are conjunctive queries. Motivated by situation awareness applications, we investigate an extension of OBDA to the temporal case. As query language we consider an extension of the well-known propositional temporal logic LTL where conjunctive queries can occur in place of propositional variables, and as ontology language we use the prototypical expressive DL ALC. For the resulting instance of temporalized OBDA, we investigate both data complexity and combined complexity of the query entailment problem.
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Borgwardt, Stefan, and Veronika Thost. Temporal Query Answering in EL. Technische Universität Dresden, 2015. http://dx.doi.org/10.25368/2022.214.

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Context-aware systems use data about their environment for adaptation at runtime, e.g., for optimization of power consumption or user experience. Ontology-based data access (OBDA) can be used to support the interpretation of the usually large amounts of data. OBDA augments query answering in databases by dropping the closed-world assumption (i.e., the data is not assumed to be complete any more) and by including domain knowledge provided by an ontology. We focus on a recently proposed temporalized query language that allows to combine conjunctive queries with the operators of the well-known propositional temporal logic LTL. In particular, we investigate temporalized OBDA w.r.t. ontologies in the DL EL, which allows for efficient reasoning and has been successfully applied in practice. We study both data and combined complexity of the query entailment problem.
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