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Computational reaching of quantified consequences from imperfect initial data

MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2025年第4期48卷 4232-4243页

作者： Medina, Jesus Torne-Zambrano, Jose Antonio Univ Cadiz Dept Math Cadiz Spain

Usually, it is not direct to translate theoretical results to practice. One of the challenges is the real computation of solutions to proposed problems, when infinite numbers (such as real numbers or the unit interval) are considered. The same is true when consequences (information) from a data set modeled by logical rules need to be obtained. In this framework, this information is obtained from the immediate consequences operator and ensuring its continuity is fundamental for making sure the computation of this information in a countable number of iterations. Recently, a versatile operator using generalized quantifiers has been introduced. This note will advance in the knowledge introducing necessary and sufficient conditions to ensure the continuity of this new flexible operator.

关键词： fixed-point semantics fuzzy sets generalized quantifiers immediate consequences operator

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Notes on Models of (Partial) Kripke-Feferman Truth

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STUDIA LOGICA 2023年第1期111卷 83-111页

作者： Castaldo, Luca Univ Warsaw Dept Philosophy Warsaw Poland

This article investigates models of axiomatizations related to the semantic conception of truth presented by Kripke (J Philos 72(19):690-716, 1975), the so-called fixed-point semantics. Among the various proof systems devised as a proof-theoretic characterization of the fixed-point semantics, in recent years two alternatives have received particular attention: classical systems (i.e., systems based on classical logic) and nonclassical systems (i.e., systems based on some nonclassical logic). The present article, building on Halbach and Nicolai (J Philos Log 47(2):227-257, 2018), shows that there is a sense in which classical and nonclassical theories (in suitable variants) have the same models.

关键词： Theories of truth fixed-point semantics Nonstandard models Classical and nonclassical logic KF and PKF

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Paradoxicality in Kripke's theory of truth

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SYNTHESE 2022年第2期200卷 71页

作者： Rosenblatt, Lucas Gallovich, Camila Univ Buenos Aires Natl Council Sci & Tech Res Bulnes 642 RA-1176 Buenos Aires DF Argentina Univ Buenos Aires Puan 480 Buenos Aires DF Argentina

A lot has been written on solutions to the semantic paradoxes, but very little on the topic of general theories of paradoxicality. The reason for this, we believe, is that it is not easy to disentangle a solution to the paradoxes from a specific conception of what those paradoxes consist in. This paper goes some way towards remedying this situation. We first address the question of what one should expect from an account of paradoxicality. We then present one conception of paradoxicality that has been offered in the literature: the fixed-point conception. According to this conception, a statement is paradoxical if it cannot obtain a classical truth-value at any fixed-point model. In order to assess this proposal rigorously we provide a non-metalinguistic characterization of paradoxicality and we evaluate whether the resulting account satisfies a number of reasonable desiderata.

关键词： fixed-point semantics Non-classical logic Truth Semantic paradoxes

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Founded semantics and constraint semantics of logic rules

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JOURNAL OF LOGIC AND COMPUTATION 2020年第8期30卷 1609-1638页

作者： Liu, Yanhong A. Stoller, Scott D. SUNY Stony Brook Comp Sci Dept Stony Brook NY 11794 USA

Logic rules and inference are fundamental in computer science and have been studied extensively. However, prior semantics of logic languages can have subtle implications and can disagree significantly, on even very simple programs, including in attempting to solve the well-known Russell's paradox. These semantics are often non-intuitive and hard-to-understand when unrestricted negation is used in recursion. This paper describes a simple new semantics for logic rules, founded semantics, and its straightforward extension to another simple new semantics, constraint semantics, that unify the core of different prior semantics. The new semantics support unrestricted negation, as well as unrestricted existential and universal quantifications. They are uniquely expressive and intuitive by allowing assumptions about the predicates, rules and reasoning to be specified explicitly, as simple and precise binary choices. They are completely declarative and relate cleanly to prior semantics. In addition, founded semantics can be computed in linear time in the size of the ground program.

关键词： Datalog recursion unrestricted negation existential and universal quantifications fixed-point semantics constraints well-founded semantics stable model semantics

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Founded semantics and Constraint semantics of Logic Rules

Founded Semantics and Constraint Semantics of Logic Rules

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International Symposium on Logical Foundations of Computer Science (LFCS)

作者： Liu, Yanhong A. Stoller, Scott D. SUNY Stony Brook Comp Sci Dept Stony Brook NY 11794 USA

ISBN: (纸本)9783319720562;9783319720555

Logic rules and inference are fundamental in computer science and have been studied extensively. However, prior semantics of logic languages can have subtle implications and can disagree significantly. This paper describes a simple new semantics for logic rules, founded semantics, and its straightforward extension to another simple new semantics, constraint semantics, that unify the core of different prior semantics. The new semantics support unrestricted negation, as well as unrestricted existential and universal quantifications. They are uniquely expressive and intuitive by allowing assumptions about the predicates and rules to be specified explicitly. They are completely declarative and relate cleanly to prior semantics. In addition, founded semantics can be computed in linear time in the size of the ground program.

关键词： Datalog Unrestricted negation Existential and universal quantifications fixed-point semantics Constraints Well-founded semantics Stable model semantics Fitting (Kripke-Kleene) semantics Supported model semantics

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Construction of P-Minimal Models Using Paraconsistent Relational Model 9th

Construction of P-Minimal Models Using Paraconsistent Relati...

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9th International Workshop on Multi-Disciplinary Trends in Artificial Intelligence (MIWAI)

作者： Jayakumar, Badrinath Sunderraman, Rajshekhar Georgia State Univ Dept Comp Sci Atlanta GA 30303 USA

ISBN: (纸本)9783319261812;9783319261805

Positive extended disjunctive deductive databases are those that contain explicit negation both in the head and body of the clauses. For such databases, paraconsistent minimal models (p-minimal models) have been proposed based on multi-valued logic (four-valued logic). Moreover, the paraconsistent relational model is also based on four-valued logic. In this paper, we propose an algorithm, which converts clauses to equations and solves it, to find p-minimal models using the paraconsistent relational model. In order to accomplish that, we use disjunctive paraconsistent relation model.

关键词： Inconsistency Paraconsistent relational model fixed-point semantics Four-valued logic

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Description Logic Programs: A Paraconsistent Relational Model Approach 14th

Description Logic Programs: A Paraconsistent Relational Mode...

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14th Mexican International Conference on Artificial Intelligence (MICAI)

作者： Jayakumar, Badrinath Sunderraman, Rajshekhar Georgia State Univ Dept Comp Sci Atlanta GA 30303 USA

ISBN: (纸本)9783319270609;9783319270593

A description logic program (dl-program) consists of a description logic knowledge base (a terminological box and an assertion box) and a set of rules for a logic program. For such description logic programs, instead of providing the fixed-point semantics for dl-programs by the immediate consequence operator, we propose an algorithm based on the paraconsistent relational model that mimics the immediate consequence operator of dl-programs. We also introduce a dl-paraconsistent relation (dl-relation), which is essential for sending information between description logic and logic programs represented in terms of equations containing paraconsistent relations. The first step in our algorithm is to convert rules, which may contain dl-atoms that enable the flow of information between description logic and logic programs, into paraconsistent relation equations that contain paraconsistent relational algebraic operators. The second step is to determine iteratively the fixed-point semantics for dl-programs using these equations. We will also prove the correctness of both steps of the algorithm.

关键词： Description logic Logic programs fixed-point semantics Paraconsistent relational model

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How Truth Behaves When There's No Vicious Reference

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JOURNAL OF PHILOSOPHICAL LOGIC 2010年第4期39卷 345-367页

作者： Kremer, Philip Univ Toronto Dept Philosophy Toronto ON M5R 2M8 Canada

In The Revision Theory of Truth (MIT Press), Gupta and Belnap (1993) claim as an advantage of their approach to truth "its consequence that truth behaves like an ordinary classical concept under certain conditions-conditions that can roughly be characterized as those in which there is no vicious reference in the language." To clarify this remark, they define Thomason models, nonpathological models in which truth behaves like a classical concept, and investigate conditions under which a model is Thomason: they argue that a model is Thomason when there is no vicious reference in it. We extend their investigation, considering notions of nonpathologicality and senses of "no vicious reference" generated both by revision theories of truth and by fixed-point theories of truth. We show that some of the fixed-point theories have an advantage analogous to that which Gupta and Belnap claim for their approach, and that at least one revision theory does not. This calls into question the claim that the revision theories have a distinctive advantage in this regard.

关键词： Truth Paradox Vicious reference fixed-point semantics Revision theory

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Epistemic foundation of stable model semantics

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THEORY AND PRACTICE OF LOGIC PROGRAMMING 2006年第4期6卷 355-393页

作者： Loyer, Yann Straccia, Umberto Univ Versailles Lab PRiSM F-78000 Versailles France CNR Ist Sci & Tecnol Informaz A Faedo Pisa Italy

Stable model semantics has become a very popular approach for the management of negation in logic programming. This approach relies mainly on the closed world assumption to complete the available knowledge and its formulation has its basis in the so-called Gelfond-Lifschitz transformation. The primary goal of this work is to present an alternative and epistemic-based characterization of stable model semantics, to the Gelfond-Lifschitz transformation. In particular, we show that stable model semantics can be defined entirely as an extension of the Kripke-Kleene semantics. Indeed, we show that the closed world assumption can be seen as an additional source of 'falsehood' to be added cumulatively to the Kripke-Kleene semantics. Our approach is purely algebraic and can abstract from the particular formalism of choice as it is based on monotone operators (under the knowledge order) over bilattices only.

关键词： bilattices fixed-point semantics logic programs stable model semantics non-monotonic reasoning

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Generalized metrics and uniquely determined logic programs

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THEORETICAL COMPUTER SCIENCE 2003年第1-3期305卷 187-219页

作者： Hitzler, P Seda, AK Natl Univ Ireland Univ Coll Cork Dept Math Cork Ireland

The introduction of negation into logic programming brings the benefit of enhanced syntax and expressibility, but creates some semantical problems. Specifically, certain operators which are monotonic in the absence of negation become non-monotonic when it is introduced, with the result that standard approaches to denotational semantics then become inapplicable. In this paper, we show how generalized metric spaces can be used to obtain fixed-point semantics for several classes of programs relative to the supported model semantics, and investigate relationships between the underlying spaces we employ. Our methods allow the analysis of classes of programs which include the acyclic, locally hierarchical, and acceptable programs, amongst others, and draw on fixed-point theorems which apply to generalized ultrametric spaces and to partial metric spaces. (C) 2002 Elsevier B.V. All rights reserved.

关键词： logic programming generalized metric domain theory Clark completion fixed-point semantics

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