Results for 'tableaux'

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  1. Tableaux-based decision method for single-agent linear time synchronous temporal epistemic logics with interacting time and knowledge.Mai Ajspur & Valentin Goranko - 2013 - In Kamal Lodaya (ed.), Logic and its Applications. Springer. pp. 80--96.
    Temporal epistemic logics are known, from results of Halpern and Vardi, to have a wide range of complexities of the satisfiability problem: from PSPACE, through non-elementary, to highly undecidable. These complexities depend on the choice of some key parameters specifying, inter alia, possible interactions between time and knowledge, such as synchrony and agents' abilities for learning and recall. In this work we develop practically implementable tableau-based decision procedures for deciding satisfiability in single-agent synchronous temporal-epistemic logics with interactions between time and (...)
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  2. Dynamic Tableaux for Dynamic Modal Logics.Jonas De Vuyst - 2013 - Dissertation, Vrije Universiteit Brussel
    In this dissertation we present proof systems for several modal logics. These proof systems are based on analytic (or semantic) tableaux. -/- Modal logics are logics for reasoning about possibility, knowledge, beliefs, preferences, and other modalities. Their semantics are almost always based on Saul Kripke’s possible world semantics. In Kripke semantics, models are represented by relational structures or, equivalently, labeled graphs. Syntactic formulas that express statements about knowledge and other modalities are evaluated in terms of such models. -/- This (...)
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  3. Tableaux sin refutación.Tomás Barrero & Walter Carnielli - 2005 - Matemáticas: Enseñanza Universitaria 13 (2):81-99.
    Motivated by H. Curry’s well-known objection and by a proposal of L. Henkin, this article introduces the positive tableaux, a form of tableau calculus without refutation based upon the idea of implicational triviality. The completeness of the method is proven, which establishes a new decision procedure for the (classical) positive propositional logic. We also introduce the concept of paratriviality in order to contribute to the question of paradoxes and limitations imposed by the behavior of classical implication.
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  4. Analytic Tableaux for all of SIXTEEN 3.Stefan Wintein & Reinhard Muskens - 2015 - Journal of Philosophical Logic 44 (5):473-487.
    In this paper we give an analytic tableau calculus P L 1 6 for a functionally complete extension of Shramko and Wansing’s logic. The calculus is based on signed formulas and a single set of tableau rules is involved in axiomatising each of the four entailment relations ⊧ t, ⊧ f, ⊧ i, and ⊧ under consideration—the differences only residing in initial assignments of signs to formulas. Proving that two sets of formulas are in one of the first three entailment (...)
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  5. Non-Analytic Tableaux for Chellas's Conditional Logic CK and Lewis's Logic of Counterfactuals VC.Richard Zach - 2018 - Australasian Journal of Logic 15 (3):609-628.
    Priest has provided a simple tableau calculus for Chellas's conditional logic Ck. We provide rules which, when added to Priest's system, result in tableau calculi for Chellas's CK and Lewis's VC. Completeness of these tableaux, however, relies on the cut rule.
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  6.  76
    A Technique for Determing Closure in Semantic Tableaux.Steven James Bartlett - 1983 - Methodology and Science: Interdisciplinary Journal for the Empirical Study of the Foundations of Science and Their Methodology 16 (1):1-16.
    The author considers the model-theoretic character of proofs and disproofs by means of attempted counterexample constructions, distinguishes this proof format from formal derivations, then contrasts two approaches to semantic tableaux proposed by Beth and Lambert-van Fraassen. It is noted that Beth's original approach has not as yet been provided with a precisely formulated rule of closure for detecting tableau sequences terminating in contradiction. To remedy this deficiency, a technique is proposed to clarify tableau operations.
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  7. Dual Systems of Sequents and Tableaux for Many-Valued Logics.Matthias Baaz, Christian G. Fermüller & Richard Zach - 1993 - Bulletin of the EATCS 51:192-197.
    The aim of this paper is to emphasize the fact that for all finitely-many-valued logics there is a completely systematic relation between sequent calculi and tableau systems. More importantly, we show that for both of these systems there are al- ways two dual proof sytems (not just only two ways to interpret the calculi). This phenomenon may easily escape one’s attention since in the classical (two-valued) case the two systems coincide. (In two-valued logic the assignment of a truth value and (...)
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  8. Recognizing Argument Types and Adding Missing Reasons.Christoph Lumer - 2019 - In Bart J. Garssen, David Godden, Gordon Mitchell & Jean Wagemans (eds.), Proceedings of the Ninth Conference of the International Society for the Study of Argumentation (ISSA). [Amsterdam, July 3-6, 2018.]. Amsterdam (Netherlands): pp. 769-777.
    The article develops and justifies, on the basis of the epistemological argumentation theory, two central pieces of the theory of evaluative argumentation interpretation: 1. criteria for recognizing argument types and 2. rules for adding reasons to create ideal arguments. Ad 1: The criteria for identifying argument types are a selection of essential elements from the definitions of the respective argument types. Ad 2: After presenting the general principles for adding reasons (benevolence, authenticity, immanence, optimization), heuristics are proposed for finding missing (...)
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  9. Proof Theory of Finite-valued Logics.Richard Zach - 1993 - Dissertation, Technische Universität Wien
    The proof theory of many-valued systems has not been investigated to an extent comparable to the work done on axiomatizatbility of many-valued logics. Proof theory requires appropriate formalisms, such as sequent calculus, natural deduction, and tableaux for classical (and intuitionistic) logic. One particular method for systematically obtaining calculi for all finite-valued logics was invented independently by several researchers, with slight variations in design and presentation. The main aim of this report is to develop the proof theory of finite-valued first (...)
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  10. From Bi-facial Truth to Bi-facial Proofs.Stefan Wintein & Reinhard A. Muskens - 2015 - Studia Logica 103 (3):545-558.
    In their recent paper Bi-facial truth: a case for generalized truth values Zaitsev and Shramko [7] distinguish between an ontological and an epistemic interpretation of classical truth values. By taking the Cartesian product of the two disjoint sets of values thus obtained, they arrive at four generalized truth values and consider two “semi-classical negations” on them. The resulting semantics is used to define three novel logics which are closely related to Belnap’s well-known four valued logic. A syntactic characterization of these (...)
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  11. Introduction to Mathematical Logic, Edition 2021.Vilnis Detlovs & Karlis Podnieks - manuscript
    Textbook for students in mathematical logic. Part 1. Total formalization is possible! Formal theories. First order languages. Axioms of constructive and classical logic. Proving formulas in propositional and predicate logic. Glivenko's theorem and constructive embedding. Axiom independence. Interpretations, models and completeness theorems. Normal forms. Tableaux method. Resolution method. Herbrand's theorem.
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  12.  46
    A Modal Logic to Reason about Analogical Proportion.José David García Cruz - 2016 - Studia Metodologiczne 37 (1):73-96.
    A modal logic for representing analogical proportions is presented. This logic is a modal interpretation of H. Prade and G. Richard's homogeneous analogy. A tableaux system is given with some examples an intuitions.
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  13. Epimorphism between Fine and Ferguson’s Matrices for Angell’s AC.Richard Zach - forthcoming - Logic and Logical Philosophy:1-19.
    Angell's logic of analytic containment AC has been shown to be characterized by a 9-valued matrix NC by Ferguson, and by a 16-valued matrix by Fine. We show that the former is the image of a surjective homomorphism from the latter, i.e., an epimorphic image. The epimorphism was found with the help of MUltlog, which also provides a tableau calculus for NC extended by quantifiers that generalize conjunction and disjunction.
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  14.  24
    Towards Tractable Approximations to Many-Valued Logics: the Case of First Degree Entailment.Alejandro Solares-Rojas & Marcello D’Agostino - 2022 - In Igor Sedlár (ed.), The Logica Yearbook, 2021. London, UK: pp. 57-76.
    FDE is a logic that captures relevant entailment between implication-free formulae and admits of an intuitive informational interpretation as a 4-valued logic in which “a computer should think”. However, the logic is co-NP complete, and so an idealized model of how an agent can think. We address this issue by shifting to signed formulae where the signs express imprecise values associated with two distinct bipartitions of the set of standard 4 values. Thus, we present a proof system which consists of (...)
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  15. Boxes and Diamonds: An Open Introduction to Modal Logic.Richard Zach - 2019 - Open Logic Project.
    A textbook for modal and other intensional logics based on the Open Logic Project. It covers normal modal logics, relational semantics, axiomatic and tableaux proof systems, intuitionistic logic, and counterfactual conditionals.
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  16. Many-valued logics. A mathematical and computational introduction.Luis M. Augusto - 2020 - London: College Publications.
    2nd edition. Many-valued logics are those logics that have more than the two classical truth values, to wit, true and false; in fact, they can have from three to infinitely many truth values. This property, together with truth-functionality, provides a powerful formalism to reason in settings where classical logic—as well as other non-classical logics—is of no avail. Indeed, originally motivated by philosophical concerns, these logics soon proved relevant for a plethora of applications ranging from switching theory to cognitive modeling, and (...)
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  17. Tableau-based decision procedure for the multiagent epistemic logic with all coalitional operators for common and distributed knowledge.M. Ajspur, V. Goranko & D. Shkatov - 2013 - Logic Journal of the IGPL 21 (3):407-437.
    We develop a conceptually clear, intuitive, and feasible decision procedure for testing satisfiability in the full multi\-agent epistemic logic \CMAELCD\ with operators for common and distributed knowledge for all coalitions of agents mentioned in the language. To that end, we introduce Hintikka structures for \CMAELCD\ and prove that satisfiability in such structures is equivalent to satisfiability in standard models. Using that result, we design an incremental tableau-building procedure that eventually constructs a satisfying Hintikka structure for every satisfiable input set of (...)
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  18. Logical consequence in modal logic II: Some semantic systems for S4.George Weaver - 1974 - Notre Dame Journal of Formal Logic 15:370.
    ABSTRACT: This 1974 paper builds on our 1969 paper (Corcoran-Weaver [2]). Here we present three (modal, sentential) logics which may be thought of as partial systematizations of the semantic and deductive properties of a sentence operator which expresses certain kinds of necessity. The logical truths [sc. tautologies] of these three logics coincide with one another and with those of standard formalizations of Lewis's S5. These logics, when regarded as logistic systems (cf. Corcoran [1], p. 154), are seen to be equivalent; (...)
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  19. Três Vezes Não: Um Estudo Sobre as Negações Clássica, Paraconsistente e Paracompleta.Kherian Gracher - 2020 - Dissertation, Federal University of Santa Catarina
    Could there be a single logical system that would allow us to work simultaneously with classical, paraconsistent, and paracomplete negations? These three negations were separately studied in logics whose negations bear their names. Initially we will restrict our analysis to propositional logics by analyzing classical negation, ¬c, as treated by Classical Propositional Logic (LPC); the paraconsistent negation, ¬p, as treated through the hierarchy of Paraconsistent Propositional Calculi Cn (0 ≤ n ≤ ω); and the paracomplete negation, ¬q, as treated by (...)
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  20. Ways Modality Could Be.Jason Zarri - manuscript
    In this paper I introduce the idea of a higher-order modal logic—not a modal logic for higher-order predicate logic, but rather a logic of higher-order modalities. “What is a higher-order modality?”, you might be wondering. Well, if a first-order modality is a way that some entity could have been—whether it is a mereological atom, or a mereological complex, or the universe as a whole—a higher-order modality is a way that a first-order modality could have been. First-order modality is modeled in (...)
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  21. A general tableau method for propositional interval temporal logics: Theory and implementation.V. Goranko, A. Montanari, P. Sala & G. Sciavicco - 2006 - Journal of Applied Logic 4 (3):305-330.
    In this paper we focus our attention on tableau methods for propositional interval temporal logics. These logics provide a natural framework for representing and reasoning about temporal properties in several areas of computer science. However, while various tableau methods have been developed for linear and branching time point-based temporal logics, not much work has been done on tableau methods for interval-based ones. We develop a general tableau method for Venema's \cdt\ logic interpreted over partial orders (\nsbcdt\ for short). It combines (...)
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  22. Lógica positiva : plenitude, potencialidade e problemas (do pensar sem negação).Tomás Barrero - 2004 - Dissertation, Universidade Estadual de Campinas
    This work studies some problems connected to the role of negation in logic, treating the positive fragments of propositional calculus in order to deal with two main questions: the proof of the completeness theorems in systems lacking negation, and the puzzle raised by positive paradoxes like the well-known argument of Haskel Curry. We study the constructive com- pleteness method proposed by Leon Henkin for classical fragments endowed with implication, and advance some reasons explaining what makes difficult to extend this constructive (...)
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  23.  62
    Proof Theory and Semantics for a Theory of Definite Descriptions.Nils Kürbis - 2021 - In Anupam Das & Sara Negri (eds.), TABLEAUX 2021, LNAI 12842.
    This paper presents a sequent calculus and a dual domain semantics for a theory of definite descriptions in which these expressions are formalised in the context of complete sentences by a binary quantifier I. I forms a formula from two formulas. Ix[F, G] means ‘The F is G’. This approach has the advantage of incorporating scope distinctions directly into the notation. Cut elimination is proved for a system of classical positive free logic with I and it is shown to be (...)
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  24.  81
    Nested Sequents for Intuitionistic Modal Logics via Structural Refinement.Tim Lyon - 2021 - In Anupam Das & Sara Negri (eds.), Automated Reasoning with Analytic Tableaux and Related Methods: TABLEAUX 2021. 93413 Cham, Germany: pp. 409-427.
    We employ a recently developed methodology -- called "structural refinement" -- to extract nested sequent systems for a sizable class of intuitionistic modal logics from their respective labelled sequent systems. This method can be seen as a means by which labelled sequent systems can be transformed into nested sequent systems through the introduction of propagation rules and the elimination of structural rules, followed by a notational translation. The nested systems we obtain incorporate propagation rules that are parameterized with formal grammars, (...)
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