Results for 'Soundness and completeness theorems'

976 found
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  1.  55
    Normalization, Soundness and Completeness for the Propositional Fragment of Prawitz’ Ecumenical System.Luiz Carlos Pereira & Ricardo Oscar Rodriguez - 2017 - Revista Portuguesa de Filosofia 73 (3-4):1153-1168.
    In 2015 Dag Prawitz proposed an Ecumenical system where classical and intuitionistic logic could coexist in peace. The classical logician and the intuitionistic logician would share the universal quantifier, conjunction, negation and the constant for the absurd, but they would each have their own existential quantifier, disjunction and implication, with different meanings. Prawitz’ main idea is that these different meanings are given by a semantical framework that can be accepted by both parties. The aim of the present paper is [1] (...)
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  2. Logical Consequence and First-Order Soundness and Completeness: A Bottom Up Approach.Eli Dresner - 2011 - Notre Dame Journal of Formal Logic 52 (1):75-93.
    What is the philosophical significance of the soundness and completeness theorems for first-order logic? In the first section of this paper I raise this question, which is closely tied to current debate over the nature of logical consequence. Following many contemporary authors' dissatisfaction with the view that these theorems ground deductive validity in model-theoretic validity, I turn to measurement theory as a source for an alternative view. For this purpose I present in the second section several (...)
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  3.  37
    Completeness and Herbrand Theorems for Nominal Logic.James Cheney - 2006 - Journal of Symbolic Logic 71 (1):299 - 320.
    Nominal logic is a variant of first-order logic in which abstract syntax with names and binding is formalized in terms of two basic operations: name-swapping and freshness. It relies on two important principles: equivariance (validity is preserved by name-swapping), and fresh name generation ("new" or fresh names can always be chosen). It is inspired by a particular class of models for abstract syntax trees involving names and binding, drawing on ideas from Fraenkel-Mostowski set theory: finite-support models in which each value (...)
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  4.  23
    A completeness theorem for continuous predicate modal logic.Stefano Baratella - 2019 - Archive for Mathematical Logic 58 (1-2):183-201.
    We study a modal extension of the Continuous First-Order Logic of Ben Yaacov and Pedersen :168–190, 2010). We provide a set of axioms for such an extension. Deduction rules are just Modus Ponens and Necessitation. We prove that our system is sound with respect to a Kripke semantics and, building on Ben Yaacov and Pedersen, that it satisfies a number of properties similar to those of first-order predicate logic. Then, by means of a canonical model construction, we get that every (...)
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  5.  53
    On the way to a Wider model theory: Completeness theorems for first-order logics of formal inconsistency.Walter Carnielli, Marcelo E. Coniglio, Rodrigo Podiacki & Tarcísio Rodrigues - 2014 - Review of Symbolic Logic 7 (3):548-578.
    This paper investigates the question of characterizing first-order LFIs (logics of formal inconsistency) by means of two-valued semantics. LFIs are powerful paraconsistent logics that encode classical logic and permit a finer distinction between contradictions and inconsistencies, with a deep involvement in philosophical and foundational questions. Although focused on just one particular case, namely, the quantified logic QmbC, the method proposed here is completely general for this kind of logics, and can be easily extended to a large family of quantified paraconsistent (...)
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  6. Truthmakers, Incompatibility, and Modality.Matteo Plebani, Giuliano Rosella & Vita Saitta - 2022 - Australasian Journal of Logic 19 (5):214–253.
    This paper introduces a new framework, based on the notion of compatibility space, obtained by adding a primitive incompatibility relation to a state space in the sense of Fine. The key idea inspiring the framework is to modify Fine's truthmaker semantics by taking the notion of incompatibility as primitive, and use it to define other notions. We discuss some interesting features of the framework and explore its advantages over the standard framework of state spaces. We review some applications of the (...)
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  7.  14
    On a Four-Valued Logic of Formal Inconsistency and Formal Undeterminedness.Marcelo E. Coniglio, G. T. Gomez–Pereira & Martín Figallo - forthcoming - Studia Logica:1-42.
    Belnap–Dunn’s relevance logic, \(\textsf{BD}\), was designed seeking a suitable logical device for dealing with multiple information sources which sometimes may provide inconsistent and/or incomplete pieces of information. \(\textsf{BD}\) is a four-valued logic which is both paraconsistent and paracomplete. On the other hand, De and Omori, while investigating what classical negation amounts to in a paracomplete and paraconsistent four-valued setting, proposed the expansion \(\textsf{BD2}\) of the four valued Belnap–Dunn logic by a classical negation. In this paper, we introduce a four-valued expansion (...)
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  8.  63
    Exactly true and non-falsity logics meeting infectious ones.Alex Belikov & Yaroslav Petrukhin - 2020 - Journal of Applied Non-Classical Logics 30 (2):93-122.
    In this paper, we study logical systems which represent entailment relations of two kinds. We extend the approach of finding ‘exactly true’ and ‘non-falsity’ versions of four-valued logics that emerged in series of recent works [Pietz & Rivieccio (2013). Nothing but the truth. Journal of Philosophical Logic, 42(1), 125–135; Shramko (2019). Dual-Belnap logic and anything but falsehood. Journal of Logics and their Applications, 6, 413–433; Shramko et al. (2017). First-degree entailment and its relatives. Studia Logica, 105(6), 1291–1317] to the case (...)
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  9.  75
    Solovay-Type Theorems for Circular Definitions.Shawn Standefer - 2015 - Review of Symbolic Logic 8 (3):467-487.
    We present an extension of the basic revision theory of circular definitions with a unary operator, □. We present a Fitch-style proof system that is sound and complete with respect to the extended semantics. The logic of the box gives rise to a simple modal logic, and we relate provability in the extended proof system to this modal logic via a completeness theorem, using interpretations over circular definitions, analogous to Solovay’s completeness theorem forGLusing arithmetical interpretations. We adapt our (...)
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  10.  45
    Boolean Valued Models, Boolean Valuations, and Löwenheim-Skolem Theorems.Xinhe Wu - 2023 - Journal of Philosophical Logic 53 (1):293-330.
    Boolean-valued models for first-order languages generalize two-valued models, in that the value range is allowed to be any complete Boolean algebra instead of just the Boolean algebra 2. Boolean-valued models are interesting in multiple aspects: philosophical, logical, and mathematical. The primary goal of this paper is to extend a number of critical model-theoretic notions and to generalize a number of important model-theoretic results based on these notions to Boolean-valued models. For instance, we will investigate (first-order) Boolean valuations, which are natural (...)
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  11.  22
    A completeness result for a realisability semantics for an intersection type system.Fairouz Kamareddine & Karim Nour - 2007 - Annals of Pure and Applied Logic 146 (2):180-198.
    In this paper we consider a type system with a universal type $omega$ where any term (whether open or closed, $beta$-normalising or not) has type $omega$. We provide this type system with a realisability semantics where an atomic type is interpreted as the set of $lambda$-terms saturated by a certain relation. The variation of the saturation relation gives a number of interpretations to each type. We show the soundness and completeness of our semantics and that for different notions (...)
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  12.  32
    Foundations of a theorem prover for functional and mathematical uses.Javier Leach & Susana Nieva - 1993 - Journal of Applied Non-Classical Logics 3 (1):7-38.
    ABSTRACT A computational logic, PLPR (Predicate Logic using Polymorphism and Recursion) is presented. Actually this logic is the object language of an automated deduction system designed as a tool for proving mathematical theorems as well as specify and verify properties of functional programs. A useful denotationl semantics and two general deduction methods for PLPR are defined. The first one is a tableau algorithm proved to be complete and also used as a guideline for building complete calculi. The second is (...)
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  13.  48
    A Sound and Complete Tableaux Calculus for Reichenbach’s Quantum Mechanics Logic.Pablo Caballero & Pablo Valencia - 2024 - Journal of Philosophical Logic 53 (1):223-245.
    In 1944 Hans Reichenbach developed a three-valued propositional logic (RQML) in order to account for certain causal anomalies in quantum mechanics. In this logic, the truth-value _indeterminate_ is assigned to those statements describing physical phenomena that cannot be understood in causal terms. However, Reichenbach did not develop a deductive calculus for this logic. The aim of this paper is to develop such a calculus by means of First Degree Entailment logic (FDE) and to prove it sound and complete with respect (...)
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  14.  38
    Arithmetical Soundness and Completeness for $$\varvec{\Sigma }_{\varvec{2}}$$ Numerations.Taishi Kurahashi - 2018 - Studia Logica 106 (6):1181-1196.
    We prove that for each recursively axiomatized consistent extension T of Peano Arithmetic and \, there exists a \ numeration \\) of T such that the provability logic of the provability predicate \\) naturally constructed from \\) is exactly \ \rightarrow \Box p\). This settles Sacchetti’s problem affirmatively.
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  15.  81
    Relational semantics and a relational proof system for full Lambek calculus.Wendy MacCaull - 1998 - Journal of Symbolic Logic 63 (2):623-637.
    In this paper we give relational semantics and an accompanying relational proof theory for full Lambek calculus (a sequent calculus which we denote by FL). We start with the Kripke semantics for FL as discussed in [11] and develop a second Kripke-style semantics, RelKripke semantics, as a bridge to relational semantics. The RelKripke semantics consists of a set with two distinguished elements, two ternary relations and a list of conditions on the relations. It is accompanied by a Kripke-style valuation system (...)
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  16.  24
    A Logic for Trial and Error Classifiers.Martin Kaså - 2015 - Journal of Logic, Language and Information 24 (3):307-322.
    Trial and error classifiers, corresponding to concepts which change their extensions over time, are introduced and briefly philosophically motivated. A fragment of the language of classical first-order logic is given a new semantics, using \-sequences of classical models, in order to interpret the basic predicates as classifiers of this kind. It turns out that we can use a natural deduction proof system which differs from classical logic only in the conditions for application of existential elimination. Soundness and completeness (...)
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  17.  88
    A sound and complete tableau calculus for reasoning about only knowing and knowing at most.Riccardo Rosati - 2001 - Studia Logica 69 (1):171-191.
    We define a tableau calculus for the logic of only knowing and knowing at most ON, which is an extension of Levesque's logic of only knowing O. The method is based on the possible-world semantics of the logic ON, and can be considered as an extension of known tableau calculi for modal logic K45. From the technical viewpoint, the main features of such an extension are the explicit representation of "unreachable" worlds in the tableau, and an additional branch closure condition (...)
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  18.  39
    Logic for update products and steps into the past.Joshua Sack - 2010 - Annals of Pure and Applied Logic 161 (12):1431-1461.
    This paper provides a sound and complete proof system for a language that adds to Dynamic Epistemic Logic a discrete previous-time operator as well as single symbol formulas that partially reveal the most recent event that occurred. The completeness theorem is by filtration followed by model unraveling and other model transformations. Decidability follows from the completeness proof. The degree to which it is important to include the additional single symbol formulas is addressed in a discussion about the difficulties (...)
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  19.  21
    Tableaux and Interpolation for Propositional Justification Logics.Meghdad Ghari - 2024 - Notre Dame Journal of Formal Logic 65 (1):81-112.
    We present tableau proof systems for the annotated version of propositional justification logics, that is, justification logics which are formulated using annotated application operators. We show that the tableau systems are sound and complete with respect to Mkrtychev models, and some tableau systems are analytic and provide a decision procedure for the annotated justification logics. We further show Craig’s interpolation property and Beth’s definability theorem for some annotated justification logics.
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  20.  33
    Boolean-Valued Models and Their Applications.Xinhe Wu - 2022 - Bulletin of Symbolic Logic 28 (4):533-533.
    Boolean-valued models generalize classical two-valued models by allowing arbitrary complete Boolean algebras as value ranges. The goal of my dissertation is to study Boolean-valued models and explore their philosophical and mathematical applications.In Chapter 1, I build a robust theory of first-order Boolean-valued models that parallels the existing theory of two-valued models. I develop essential model-theoretic notions like “Boolean-valuation,” “diagram,” and “elementary diagram,” and prove a series of theorems on Boolean-valued models, including the (strengthened) Soundness and Completeness Theorem, (...)
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  21.  30
    An Escape From Vardanyan’s Theorem.Ana de Almeida Borges & Joost J. Joosten - 2023 - Journal of Symbolic Logic 88 (4):1613-1638.
    Vardanyan’s Theorems [36, 37] state that $\mathsf {QPL}(\mathsf {PA})$ —the quantified provability logic of Peano Arithmetic—is $\Pi ^0_2$ complete, and in particular that this already holds when the language is restricted to a single unary predicate. Moreover, Visser and de Jonge [38] generalized this result to conclude that it is impossible to computably axiomatize the quantified provability logic of a wide class of theories. However, the proof of this fact cannot be performed in a strictly positive signature. The system (...)
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  22.  29
    Kripke models and the (in)equational logic of the second-order λ-calculus.Jean Gallier - 1997 - Annals of Pure and Applied Logic 84 (3):257-316.
    We define a new class of Kripke structures for the second-order λ-calculus, and investigate the soundness and completeness of some proof systems for proving inequalities as well as equations. The Kripke structures under consideration are equipped with preorders that correspond to an abstract form of reduction, and they are not necessarily extensional. A novelty of our approach is that we define these structures directly as functors A: → Preor equipped with certain natural transformations corresponding to application and abstraction (...)
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  23.  16
    Reductive Logic, Proof-Search, and Coalgebra: A Perspective from Resource Semantics.Alexander V. Gheorghiu, Simon Docherty & David J. Pym - 2023 - In Alessandra Palmigiano & Mehrnoosh Sadrzadeh (eds.), Samson Abramsky on Logic and Structure in Computer Science and Beyond. Springer Verlag. pp. 833-875.
    The reductive, as opposed to deductive, view of logic is the form of logic that is, perhaps, most widely employed in practical reasoning. In particular, it is the basis of logic programming. Here, building on the idea of uniform proof in reductive logic, we give a treatment of logic programming for BI, the logic of bunched implications, giving both operational and denotational semantics, together with soundness and completeness theorems, all couched in terms of the resource interpretation of (...)
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  24.  38
    Hybrid Formulas and Elementarily Generated Modal Logics.Ian Hodkinson - 2006 - Notre Dame Journal of Formal Logic 47 (4):443-478.
    We characterize the modal logics of elementary classes of Kripke frames as precisely those modal logics that are axiomatized by modal axioms synthesized in a certain effective way from "quasi-positive" sentences of hybrid logic. These are pure positive hybrid sentences with arbitrary existential and relativized universal quantification over nominals. The proof has three steps. The first step is to use the known result that the modal logic of any elementary class of Kripke frames is also the modal logic of the (...)
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  25.  45
    A sound and complete axiomatization for Dynamic Topological Logic.David Fernández-Duque - 2012 - Journal of Symbolic Logic 77 (3):947-969.
    Dynamic Topological Logic (DFH) is a multimodal system for reasoning about dynamical systems. It is defined semantically and, as such, most of the work done in the field has been model-theoretic. In particular, the problem of finding a complete axiomatization for the full language of DFH over the class of all dynamical systems has proven to be quite elusive. Here we propose to enrich the language to include a polyadic topological modality, originally introduced by Dawar and Otto in a different (...)
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  26.  31
    The Logic of Uncertain Justifications.Robert S. Milnikel - 2014 - Annals of Pure and Applied Logic 165 (1):305-315.
    In Artemovʼs Justification Logic, one can make statements interpreted as “t is evidence for the truth of formula F.” We propose a variant of this logic in which one can say “I have degree r of confidence that t is evidence for the truth of formula F.” After defining both an axiomatic approach and a semantics for this Logic of Uncertain Justifications, we will prove the usual soundness and completeness theorems.
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  27.  63
    Natural Deduction Calculi and Sequent Calculi for Counterfactual Logics.Francesca Poggiolesi - 2016 - Studia Logica 104 (5):1003-1036.
    In this paper we present labelled sequent calculi and labelled natural deduction calculi for the counterfactual logics CK + {ID, MP}. As for the sequent calculi we prove, in a semantic manner, that the cut-rule is admissible. As for the natural deduction calculi we prove, in a purely syntactic way, the normalization theorem. Finally, we demonstrate that both calculi are sound and complete with respect to Nute semantics [12] and that the natural deduction calculi can be effectively transformed into the (...)
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  28.  24
    Validity and quantification in intuitionism.H. C. M. de Swart & C. J. Posy - 1981 - Journal of Philosophical Logic 10 (1):117-126.
    We distinguish three different readings of the intuitionistic notions of validity, soundness, and completeness with respect to the quantification occurring in the notion of validity, and we establish certain relations between the different readings. For each of the meta-logical notions considered we suggest that the “most natural” reading (which is not the same for all cases) is precisely the one which is required by the recent intuitionistic completeness theorems for IPC.
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  29.  72
    Rules in relevant logic - I: Semantic classification.Ross T. Brady - 1994 - Journal of Philosophical Logic 23 (2):111 - 137.
    We provide five semantic preservation properties which apply to the various rules -- primitive, derived and admissible -- of Hilbert-style axiomatizations of relevant logics. These preservation properties are with respect to the Routley-Meyer semantics, and consist of various truth- preservations and validity-preservations from the premises to the conclusions of these rules. We establish some deduction theorems, some persistence theorems and some soundness and completeness theorems, for these preservation properties. We then apply the above ideas, as (...)
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  30.  35
    Categories with families and first-order logic with dependent sorts.Erik Palmgren - 2019 - Annals of Pure and Applied Logic 170 (12):102715.
    First-order logic with dependent sorts, such as Makkai's first-order logic with dependent sorts (FOLDS), or Aczel's and Belo's dependently typed (intuitionistic) first-order logic (DFOL), may be regarded as logic enriched dependent type theories. Categories with families (cwfs) is an established semantical structure for dependent type theories, such as Martin-Löf type theory. We introduce in this article a notion of hyperdoctrine over a cwf, and show how FOLDS and DFOL fit in this semantical framework. A soundness and completeness theorem (...)
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  31.  20
    Three-valued Kripke-style Semantics For Pseudo- And Weak-boolean Logics.Eunsuk Yang - 2012 - Logic Journal of the IGPL 20 (1):187-206.
    This article investigates Kripke-style semantics for two sorts of logics: pseudo-Boolean and weak-Boolean logics. As examples of the first, we introduce G3 and S53pB.G3 is the three-valued Dummett–Gödel logic; S53pB is the modal logic S5 but with its orthonegation replaced by a pB negation. Examples of wB logic are G3wB and S53wB.G3wB is G3 with a wB negation in place of its pB negation; S53wB is S5 with a wB negation replacing its orthonegation. For each system, we provide a three-valued (...)
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  32.  29
    Native diagrammatic soundness and completeness proofs for Peirce’s Existential Graphs (Alpha).Fernando Tohmé, Rocco Gangle & Gianluca Caterina - 2022 - Synthese 200 (6).
    Peirce’s diagrammatic system of Existential Graphs (EGα)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$EG_{\alpha })$$\end{document} is a logical proof system corresponding to the Propositional Calculus (PL). Most known proofs of soundness and completeness for EGα\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$EG_{\alpha }$$\end{document} depend upon a translation of Peirce’s diagrammatic syntax into that of a suitable Frege-style system. In this paper, drawing upon standard results but using the native diagrammatic notational framework of the graphs, (...)
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  33. On the logic of common belief and common knowledge.Luc Lismont & Philippe Mongin - 1994 - Theory and Decision 37 (1):75-106.
    The paper surveys the currently available axiomatizations of common belief (CB) and common knowledge (CK) by means of modal propositional logics. (Throughout, knowledge- whether individual or common- is defined as true belief.) Section 1 introduces the formal method of axiomatization followed by epistemic logicians, especially the syntax-semantics distinction, and the notion of a soundness and completeness theorem. Section 2 explains the syntactical concepts, while briefly discussing their motivations. Two standard semantic constructions, Kripke structures and neighbourhood structures, are introduced (...)
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  34.  29
    Base-extension semantics for modal logic.Timo Eckhardt & David J. Pym - forthcoming - Logic Journal of the IGPL.
    In proof-theoretic semantics, meaning is based on inference. It may seen as the mathematical expression of the inferentialist interpretation of logic. Much recent work has focused on base-extension semantics, in which the validity of formulas is given by an inductive definition generated by provability in a ‘base’ of atomic rules. Base-extension semantics for classical and intuitionistic propositional logic have been explored by several authors. In this paper, we develop base-extension semantics for the classical propositional modal systems |$K$|⁠, |$KT$|⁠, |$K4$| and (...)
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  35.  27
    Polymodal Lattices and Polymodal Logic.John L. Bell - 1996 - Mathematical Logic Quarterly 42 (1):219-233.
    A polymodal lattice is a distributive lattice carrying an n-place operator preserving top elements and certain finite meets. After exploring some of the basic properties of such structures, we investigate their freely generated instances and apply the results to the corresponding logical systems — polymodal logics — which constitute natural generalizations of the usual systems of modal logic familiar from the literature. We conclude by formulating an extension of Kripke semantics to classical polymodal logic and proving soundness and (...) theorems. (shrink)
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  36.  28
    A Sound And Complete Deductive System For Ctl* Verification.Dov Gabbay - 2008 - Logic Journal of the IGPL 16 (6):499-536.
    The paper presents a compositional approach to the verification of CTL* properties over reactive systems. Both symbolic model-checking and deductive verification are considered. Both methods are based on two decomposition principles. A general state formula is decomposed into basic state formulas which are CTL* formulas with no embedded path quantifiers. To deal with arbitrary basic state formulas, we introduce another reduction principle which replaces each basic path formula, i.e., path formulas whose principal operator is temporal and which contain no embedded (...)
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  37. Fusion, fission, and Ackermann’s truth constant in relevant logics: A proof-theoretic investigation.Fabio De Martin Polo - 2024 - In Andrew Tedder, Shawn Standefer & Igor Sedlar (eds.), New Directions in Relevant Logic. Springer.
    The aim of this paper is to provide a proof-theoretic characterization of relevant logics including fusion and fission connectives, as well as Ackermann’s truth constant. We achieve this by employing the well-established methodology of labelled sequent calculi. After having introduced several systems, we will conduct a detailed proof-theoretic analysis, show a cut-admissibility theorem, and establish soundness and completeness. The paper ends with a discussion that contextualizes our current work within the broader landscape of the proof theory of relevant (...)
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  38. One-step Modal Logics, Intuitionistic and Classical, Part 1.Harold T. Hodes - 2021 - Journal of Philosophical Logic 50 (5):837-872.
    This paper and its sequel “look under the hood” of the usual sorts of proof-theoretic systems for certain well-known intuitionistic and classical propositional modal logics. Section 1 is preliminary. Of most importance: a marked formula will be the result of prefixing a formula in a propositional modal language with a step-marker, for this paper either 0 or 1. Think of 1 as indicating the taking of “one step away from 0.” Deductions will be constructed using marked formulas. Section 2 presents (...)
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  39. Wittgensteinian Predicate Logic.Kai F. Wehmeier - 2004 - Notre Dame Journal of Formal Logic 45 (1):1-11.
    We investigate a rst-order predicate logic based on Wittgenstein's suggestion to express identity of object by identity of sign, and difference of objects by difference of signs. Hintikka has shown that predicate logic can indeed be set up in such a way; we show that it can be done nicely. More specically, we provide a perspicuous cut-free sequent calculus, as well as a Hilbert-type calculus, for Wittgensteinian predicate logic and prove soundness and completeness theorems.
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  40.  27
    A logic of graded attributes.Radim Belohlavek & Vilem Vychodil - 2015 - Archive for Mathematical Logic 54 (7-8):785-802.
    We present a logic for reasoning about attribute dependencies in data involving degrees such as a degree to which an object is red or a degree to which two objects are similar. The dependencies are of the form A ⇒ B and can be interpreted in two ways: first, in data tables with entries representing degrees to which objects have attributes ; second, in database tables where each domain is equipped with a similarity relation. We assume that the degrees form (...)
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  41.  19
    Sound and complete causal identification with latent variables given local background knowledge.Tian-Zuo Wang, Tian Qin & Zhi-Hua Zhou - 2023 - Artificial Intelligence 322 (C):103964.
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  42.  77
    Multiplicative conjunction and an algebraic meaning of contraction and weakening.A. Avron - 1998 - Journal of Symbolic Logic 63 (3):831-859.
    We show that the elimination rule for the multiplicative (or intensional) conjunction $\wedge$ is admissible in many important multiplicative substructural logics. These include LL m (the multiplicative fragment of Linear Logic) and RMI m (the system obtained from LL m by adding the contraction axiom and its converse, the mingle axiom.) An exception is R m (the intensional fragment of the relevance logic R, which is LL m together with the contraction axiom). Let SLL m and SR m be, respectively, (...)
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  43.  28
    A Non-Standard Kripke Semantics for the Minimal Deontic Logic.Edson Bezerra & Giorgio Venturi - forthcoming - Logic and Logical Philosophy:1.
    In this paper we study a new operator of strong modality ⊞, related to the non-contingency operator ∆. We then provide soundness and completeness theorems for the minimal logic of the ⊞-operator.
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  44. Boulesic logic, Deontic Logic and the Structure of a Perfectly Rational Will.Daniel Rönnedal - 2020 - Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 27 (2):187–262.
    In this paper, I will discuss boulesic and deontic logic and the relationship between these branches of logic. By ‘boulesic logic,’ or ‘the logic of the will,’ I mean a new kind of logic that deals with ‘boulesic’ concepts, expressions, sentences, arguments and systems. I will concentrate on two types of boulesic expression: ‘individual x wants it to be the case that’ and ‘individual x accepts that it is the case that.’ These expressions will be symbolised by two sentential operators (...)
     
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  45.  59
    Transitive primal infon logic.Carlos Cotrini & Yuri Gurevich - 2013 - Review of Symbolic Logic 6 (2):281-304.
    Primal infon logic was introduced in 2009 in connection with access control. In addition to traditional logic constructs, it contains unary connectives p said indispensable in the intended access control applications. Propositional primal infon logic is decidable in linear time, yet suffices for many common access control scenarios. The most obvious limitation on its expressivity is the failure of the transitivity law for implication: \$$ \to \$$ and \$$ \to \$$ do not necessarily yield \$$ \to \$$. Here we introduce (...)
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  46.  55
    Cut-free tableau calculi for some intuitionistic modal logics.Mauro Ferrari - 1997 - Studia Logica 59 (3):303-330.
    In this paper we provide cut-free tableau calculi for the intuitionistic modal logics IK, ID, IT, i.e. the intuitionistic analogues of the classical modal systems K, D and T. Further, we analyse the necessity of duplicating formulas to which rules are applied. In order to develop these calculi we extend to the modal case some ideas presented by Miglioli, Moscato and Ornaghi for intuitionistic logic. Specifically, we enlarge the language with the new signs Fc and CR near to the usual (...)
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  47.  41
    Axiomatisations of the Genuine Three-Valued Paraconsistent Logics $$mathbf {L3AG}$$ L 3 A G and $$mathbf {L3BG}$$ L 3 B G.Alejandro Hernández-Tello, Miguel Pérez-Gaspar & Verónica Borja Macías - 2021 - Logica Universalis 15 (1):87-121.
    Genuine Paraconsistent logics \ and \ were defined in 2016 by Béziau et al, including only three logical connectives, namely, negation disjunction and conjunction. Afterwards in 2017 Hernández-Tello et al, provide implications for both logics and define the logics \ and \. In this work we continue the study of these logics, providing sound and complete Hilbert-type axiomatic systems for each logic. We prove among other properties that \ and \ satisfy a restricted version of the Substitution Theorem, and that (...)
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    Constrained Pseudo-Propositional Logic.Ahmad-Saher Azizi-Sultan - 2020 - Logica Universalis 14 (4):523-535.
    Propositional logic, with the aid of SAT solvers, has become capable of solving a range of important and complicated problems. Expanding this range, to contain additional varieties of problems, is subject to the complexity resulting from encoding counting constraints in conjunctive normal form. Due to the limitation of the expressive power of propositional logic, generally, such an encoding increases the numbers of variables and clauses excessively. This work eliminates the indicated drawback by interpolating constraint symbols and the set of natural (...)
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    Epistemic Logics for Relevant Reasoners.Igor Sedlár & Pietro Vigiani - 2024 - Journal of Philosophical Logic 53 (5):1383-1411.
    We present a neighbourhood-style semantic framework for modal epistemic logic modelling agents who process information using relevant logic. The distinguishing feature of the framework in comparison to relevant modal logic is that the environment the agent is situated in is assumed to be a classical possible world. This framework generates two-layered logics combining classical logic on the propositional level with relevant logic in the scope of modal operators. Our main technical result is a general soundness and completeness theorem.
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    Sequent Calculi and Interpolation for Non-Normal Modal and Deontic Logics.Eugenio Orlandelli - forthcoming - Logic and Logical Philosophy:1.
    G3-style sequent calculi for the logics in the cube of non-normal modal logics and for their deontic extensions are studied. For each calculus we prove that weakening and contraction are height-preserving admissible, and we give a syntactic proof of the admissibility of cut. This implies that the subformula property holds and that derivability can be decided by a terminating proof search whose complexity is in Pspace. These calculi are shown to be equivalent to the axiomatic ones and, therefore, they are (...)
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