Search results for 'Predicate (Logic' (try it on Scholar)

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  1.  31
    Albert Visser (1998). Contexts in Dynamic Predicate Logic. Journal of Logic, Language and Information 7 (1):21-52.
    In this paper we introduce a notion of context for Groenendijk & Stokhof's Dynamic Predicate Logic DPL. We use these contexts to give a characterization of the relations on assignments that can be generated by composition from tests and random resettings in the case that we are working over an infinite domain. These relations are precisely the ones expressible in DPL if we allow ourselves arbitrary tests as a starting point. We discuss some possible extensions of DPL and the (...)
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  2.  11
    Christine Gaßner (1994). The Axiom of Choice in Second‐Order Predicate Logic. Mathematical Logic Quarterly 40 (4):533-546.
    The present article deals with the power of the axiom of choice within the second-order predicate logic. We investigate the relationship between several variants of AC and some other statements, known as equivalent to AC within the set theory of Zermelo and Fraenkel with atoms, in Henkin models of the one-sorted second-order predicate logic with identity without operation variables. The construction of models follows the ideas of Fraenkel and Mostowski. It is e. g. shown that the well-ordering theorem (...)
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  3.  15
    Victor N. Krivtsov (2010). An Intuitionistic Completeness Theorem for Classical Predicate Logic. Studia Logica 96 (1):109 - 115.
    This paper presents an intuitionistic proof of a statement which under a classical reading is logically equivalent to Gödel's completeness theorem for classical predicate logic.
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  4.  38
    Kai Brünnler (2006). Cut Elimination Inside a Deep Inference System for Classical Predicate Logic. Studia Logica 82 (1):51 - 71.
    Deep inference is a natural generalisation of the one-sided sequent calculus where rules are allowed to apply deeply inside formulas, much like rewrite rules in term rewriting. This freedom in applying inference rules allows to express logical systems that are difficult or impossible to express in the cut-free sequent calculus and it also allows for a more fine-grained analysis of derivations than the sequent calculus. However, the same freedom also makes it harder to carry out this analysis, in particular it (...)
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  5.  3
    Victor N. Krivtsov (2015). Semantical Completeness of First-Order Predicate Logic and the Weak Fan Theorem. Studia Logica 103 (3):623-638.
    Within a weak system \ of intuitionistic analysis one may prove, using the Weak Fan Theorem as an additional axiom, a completeness theorem for intuitionistic first-order predicate logic relative to validity in generalized Beth models as well as a completeness theorem for classical first-order predicate logic relative to validity in intuitionistic structures. Conversely, each of these theorems implies over \ the Weak Fan Theorem.
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  6. Predicate Logic (2003). L86, L93, 203,236. In Jaroslav Peregrin (ed.), Meaning: The Dynamic Turn. Elsevier Science 12--65.
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  7.  19
    Jonathan Fleischmann (2010). Syntactic Preservation Theorems for Intuitionistic Predicate Logic. Notre Dame Journal of Formal Logic 51 (2):225-245.
    We define notions of homomorphism, submodel, and sandwich of Kripke models, and we define two syntactic operators analogous to universal and existential closure. Then we prove an intuitionistic analogue of the generalized (dual of the) Lyndon-Łoś-Tarski Theorem, which characterizes the sentences preserved under inverse images of homomorphisms of Kripke models, an intuitionistic analogue of the generalized Łoś-Tarski Theorem, which characterizes the sentences preserved under submodels of Kripke models, and an intuitionistic analogue of the generalized Keisler Sandwich Theorem, which characterizes the (...)
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  8.  43
    P. F. Strawson (2004). Subject and Predicate in Logic and Grammar. Ashgate.
    P.F. Strawson's essay traces some formal characteristics of logic and grammar to their roots in general features of thought and experience.
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  9.  31
    M. J. Cresswell (2013). Predicate Metric Tense Logic for 'Now' and 'Then'. Journal of Philosophical Logic 42 (1):1-24.
    In a number of publications A.N. Prior considered the use of what he called ‘metric tense logic’. This is a tense logic in which the past and future operators P and F have an index representing a temporal distance, so that Pnα means that α was true n -much ago, and Fn α means that α will be true n -much hence. The paper investigates the use of metric predicate tense logic in formalising phenomena ormally treated by such devices (...)
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  10. Jeroen Groenendijk & Martin Stokhof (1991). Dynamic Predicate Logic. Linguistics and Philosophy 14 (1):39-100.
    This paper is devoted to the formulation and investigation of a dynamic semantic interpretation of the language of first-order predicate logic. The resulting system, which will be referred to as ‘dynamic predicate logic’, is intended as a first step towards a compositional, non-representational theory of discourse semantics. In the last decade, various theories of discourse semantics have emerged within the paradigm of model-theoretic semantics. A common feature of these theories is a tendency to do away with the principle (...)
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  11.  70
    James Hawthorne (1998). On the Logic of Nonmonotonic Conditionals and Conditional Probabilities: Predicate Logic. [REVIEW] Journal of Philosophical Logic 27 (1):1-34.
    In a previous paper I described a range of nonmonotonic conditionals that behave like conditional probability functions at various levels of probabilistic support. These conditionals were defined as semantic relations on an object language for sentential logic. In this paper I extend the most prominent family of these conditionals to a language for predicate logic. My approach to quantifiers is closely related to Hartry Field's probabilistic semantics. Along the way I will show how Field's semantics differs from a substitutional (...)
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  12.  22
    Shunsuke Yatabe (2009). Comprehension Contradicts to the Induction Within Łukasiewicz Predicate Logic. Archive for Mathematical Logic 48 (3-4):265-268.
    We introduce the simpler and shorter proof of Hajek’s theorem that the mathematical induction on ω implies a contradiction in the set theory with the comprehension principle within Łukasiewicz predicate logic Ł ${\forall}$ (Hajek Arch Math Logic 44(6):763–782, 2005) by extending the proof in (Yatabe Arch Math Logic, accepted) so as to be effective in any linearly ordered MV-algebra.
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  13.  7
    Pieter A. M. Seuren (2014). The Cognitive Ontogenesis of Predicate Logic. Notre Dame Journal of Formal Logic 55 (4):499-532.
    Since Aristotle and the Stoa, there has been a clash, worsened by modern predicate logic, between logically defined operator meanings and natural intuitions. Pragmatics has tried to neutralize the clash by an appeal to the Gricean conversational maxims. The present study argues that the pragmatic attempt has been unsuccessful. The “softness” of the Gricean explanation fails to do justice to the robustness of the intuitions concerned, leaving the relation between the principles evoked and the observed facts opaque. Moreover, there (...)
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  14. Howard Pospesel (1976). Predicate Logic.
     
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  15.  16
    Antonio Di Nola, George Georgescu & Luca Spada (2008). Forcing in Łukasiewicz Predicate Logic. Studia Logica 89 (1):111-145.
    In this paper we study the notion of forcing for Łukasiewicz predicate logic (Ł∀, for short), along the lines of Robinson’s forcing in classical model theory. We deal with both finite and infinite forcing. As regard to the former we prove a Generic Model Theorem for Ł∀, while for the latter, we study the generic and existentially complete standard models of Ł∀.
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  16.  35
    Mohammad Ardeshir (1999). A Translation of Intuitionistic Predicate Logic Into Basic Predicate Logic. Studia Logica 62 (3):341-352.
    Basic Predicate Logic, BQC, is a proper subsystem of Intuitionistic Predicate Logic, IQC. For every formula in the language {, , , , , , }, we associate two sequences of formulas 0,1,... and 0,1,... in the same language. We prove that for every sequent , there are natural numbers m, n, such that IQC , iff BQC n m. Some applications of this translation are mentioned.
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  17.  13
    Dmitrij Skvortsov (1997). Not Every "Tabular" Predicate Logic is Finitely Axiomatizable. Studia Logica 59 (3):387-396.
    An example of finite tree Mo is presented such that its predicate logic (i.e. the intermediate predicate logic characterized by the class of all predicate Kripke frames based on Mo) is not finitely axiomatizable. Hence it is shown that the predicate analogue of de Jongh - McKay - Hosoi's theorem on the finite axiomatizability of every finite intermediate propositional logic is not true.
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  18.  35
    Hajnal Andréka, István Németi & Johan van Benthem (1998). Modal Languages and Bounded Fragments of Predicate Logic. Journal of Philosophical Logic 27 (3):217-274.
    What precisely are fragments of classical first-order logic showing “modal” behaviour? Perhaps the most influential answer is that of Gabbay 1981, which identifies them with so-called “finite-variable fragments”, using only some fixed finite number of variables (free or bound). This view-point has been endorsed by many authors (cf. van Benthem 1991). We will investigate these fragments, and find that, illuminating and interesting though they are, they lack the required nice behaviour in our sense. (Several new negative results support this claim.) (...)
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  19.  52
    Kai Wehmeier (2004). Wittgensteinian Predicate Logic. 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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  20.  49
    Stefan Wölfl (1999). Combinations of Tense and Modality for Predicate Logic. Journal of Philosophical Logic 28 (4):371-398.
    In recent years combinations of tense and modality have moved intothe focus of logical research. From a philosophical point of view, logical systems combining tense and modality are of interest because these logics have a wide field of application in original philosophical issues, for example in the theory of causation, of action, etc. But until now only methods yielding completeness results for propositional languages have been developed. In view of philosophical applications, analogous results with respect to languages of predicate (...)
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  21.  37
    C. F. M. Vermeulen (1993). Sequence Semantics for Dynamic Predicate Logic. Journal of Logic, Language and Information 2 (3):217-254.
    In this paper a semantics for dynamic predicate logic is developed that uses sequence valued assignments. This semantics is compared with the usual relational semantics for dynamic predicate logic: it is shown that the most important intuitions of the usual semantics are preserved. Then it is shown that the refined semantics reflects out intuitions about information growth. Some other issues in dynamic semantics are formulated and discussed in terms of the new sequence semantics.
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  22.  82
    Maria Aloni (2005). Individual Concepts in Modal Predicate Logic. Journal of Philosophical Logic 34 (1):1 - 64.
    The article deals with the interpretation of propositional attitudes in the framework of modal predicate logic. The first part discusses the classical puzzles arising from the interplay between propositional attitudes, quantifiers and the notion of identity. After comparing different reactions to these puzzles it argues in favor of an analysis in which evaluations of de re attitudes may vary relative to the ways of identifying objects used in the context of use. The second part of the article gives this (...)
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  23.  55
    Tim Fernando (1994). Bisimulations and Predicate Logic. Journal of Symbolic Logic 59 (3):924-944.
    are considered with a view toward analyzing operational semantics from the perspective of predicate logic. The notion of a bisimulation is employed in two distinct ways: (i) as an extensional notion of equivalence on programs (or processes) generalizing input/output equivalence (at a cost exceeding II' ,over certain transition predicates computable in log space). and (ii) as a tool for analyzing the dependence of transitions on data (which can be shown to be elementary or nonelementary. depending on the formulation of (...)
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  24.  5
    Kosta Došen & Zoran Petrić (2009). Coherence in Linear Predicate Logic. Annals of Pure and Applied Logic 158 (1):125-153.
    Coherence with respect to Kelly–Mac Lane graphs is proved for categories that correspond to the multiplicative fragment without constant propositions of classical linear first-order predicate logic without or with mix. To obtain this result, coherence is first established for categories that correspond to the multiplicative conjunction–disjunction fragment with first-order quantifiers of classical linear logic, a fragment lacking negation. These results extend results of [K. Došen, Z. Petrić, Proof-Theoretical Coherence, KCL Publications , London, 2004 ; K. Došen, Z. Petrić, Proof-Net (...)
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  25.  1
    Johan van Benthem (1997). Modal Foundations for Predicate Logic. Logic Journal of the Igpl 5 (2):259-286.
    The complexity of any logical modeling reflects both the intrinsic structure of a topic described and the weight of the formal tools. Some of this weight seems inherent in even the most basic logical systems. Notably, standard predicate logic is undecidable. In this paper, we investigate ‘lighter’ versions of this general purpose tool, by modally ‘deconstructing’ the usual semantics, and locating implicit choice points in its set up. The first part sets out the interest of this program and the (...)
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  26.  31
    Peter Pagin & Dag Westerståhl (1993). Predicate Logic with Flexibly Binding Operators and Natural Language Semantics. Journal of Logic, Language and Information 2 (2):89-128.
    A new formalism for predicate logic is introduced, with a non-standard method of binding variables, which allows a compositional formalization of certain anaphoric constructions, including donkey sentences and cross-sentential anaphora. A proof system in natural deduction format is provided, and the formalism is compared with other accounts of this type of anaphora, in particular Dynamic Predicate Logic.
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  27.  19
    Dmitrij Skvortsov (2005). On the Predicate Logic of Linear Kripke Frames and Some of its Extensions. Studia Logica 81 (2):261 - 282.
    We propose a new, rather simple and short proof of Kripke-completeness for the predicate variant of Dummett's logic. Also a family of Kripke-incomplete extensions of this logic that are complete w.r.t. Kripke frames with equality (or equivalently, w.r.t. Kripke sheaves [8]), is described.
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  28.  8
    Mirjana Borisavljević (1999). A Cut-Elimination Proof in Intuitionistic Predicate Logic. Annals of Pure and Applied Logic 99 (1-3):105-136.
    In this paper we give a new proof of cut elimination in Gentzen's sequent system for intuitionistic first-order predicate logic. The point of this proof is that the elimination procedure eliminates the cut rule itself, rather than the mix rule.
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  29.  7
    Grigori Mints (2013). Epsilon Substitution for First-and Second-Order Predicate Logic. Annals of Pure and Applied Logic 164 (6):733-739.
    The epsilon substitution method was proposed by D. Hilbert as a tool for consistency proofs. A version for first order predicate logic had been described and proved to terminate in the monograph “Grundlagen der Mathematik”. As far as the author knows, there have been no attempts to extend this approach to the second order case. We discuss possible directions for and obstacles to such extensions.
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  30.  23
    Morten H. Sørensen & Paweł Urzyczyn (2010). A Syntactic Embedding of Predicate Logic Into Second-Order Propositional Logic. Notre Dame Journal of Formal Logic 51 (4):457-473.
    We give a syntactic translation from first-order intuitionistic predicate logic into second-order intuitionistic propositional logic IPC2. The translation covers the full set of logical connectives ∧, ∨, →, ⊥, ∀, and ∃, extending our previous work, which studied the significantly simpler case of the universal-implicational fragment of predicate logic. As corollaries of our approach, we obtain simple proofs of nondefinability of ∃ from the propositional connectives and nondefinability of ∀ from ∃ in the second-order intuitionistic propositional logic. We (...)
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  31.  10
    Max Cresswell (2013). Axiomatising the Prior Future in Predicate Logic. Logica Universalis 7 (1):87-101.
    Prior investigated a tense logic with an operator for ‘historical necessity’, where a proposition is necessary at a time iff it is true at that time in all worlds ‘accessible’ from that time. Axiomatisations of this logic all seem to require non-standard axioms or rules. The present paper presents an axiomatisation of a first-order version of Prior’s logic by using a predicate which enables any time to be picked out by an individual in the domain of interpretation.
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  32.  5
    Dmitrij Skvortsov (2005). The Superintuitionistic Predicate Logic of Finite Kripke Frames Is Not Recursively Axiomatizable. Journal of Symbolic Logic 70 (2):451 - 459.
    We prove that an intermediate predicate logic characterized by a class of finite partially ordered sets is recursively axiomatizable iff it is "finite", i.e., iff it is characterized by a single finite partially ordered set. Therefore, the predicate logic LFin of the class of all predicate Kripke frames with finitely many possible worlds is not recursively axiomatizable.
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  33.  5
    Michael Makkai (1995). On Gabbay's Proof of the Craig Interpolation Theorem for Intuitionistic Predicate Logic. Notre Dame Journal of Formal Logic 36 (3):364-381.
    Using the framework of categorical logic, this paper analyzes and streamlines Gabbay's semantical proof of the Craig interpolation theorem for intuitionistic predicate logic. In the process, an apparently new and interesting fact about the relation of coherent and intuitionistic logic is found.
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  34.  52
    Frank Veltman, Proof Systems for Dynamic Predicate Logic.
    The core language can be extended by defining additional logical constants. E.g., we can add ‘→’ (implication), ‘∨’ (disjunction), and ‘∀x’ (universal quantifiers). The choice of logical primitives is not as optional in DPL as it is in standard predicate logic.
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  35.  9
    Mitio Takano (1987). Embeddings Between the Elementary Ontology with an Atom and the Monadic Second-Order Predicate Logic. Studia Logica 46 (3):247 - 253.
    Let EOA be the elementary ontology augmented by an additional axiom S (S S), and let LS be the monadic second-order predicate logic. We show that the mapping which was introduced by V. A. Smirnov is an embedding of EOA into LS. We also give an embedding of LS into EOA.
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  36.  16
    Hugh Miller (1995). Tractarian Semantics for Predicate Logic. History and Philosophy of Logic 16 (2):197-215.
    It is a little understood fact that the system of formal logic presented in Wittgenstein?s Tractatusprovides the basis for an alternative general semantics for a predicate calculus that is consistent and coherent, essentially independent of the metaphysics of logical atomism, and philosophically illuminating in its own right. The purpose of this paper is threefold: to describe the general characteristics of a Tractarian-style semantics, to defend the Tractatus system against the charge of expressive incompleteness as levelled by Robert Fogelin, and (...)
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  37.  3
    G. Mints (2001). Interpolation Theorems for Intuitionistic Predicate Logic. Annals of Pure and Applied Logic 113 (1-3):225-242.
    Craig interpolation theorem implies that the derivability of X,X′ Y′ implies existence of an interpolant I in the common language of X and X′ Y′ such that both X I and I,X′ Y′ are derivable. For classical logic this extends to X,X′ Y,Y′, but for intuitionistic logic there are counterexamples. We present a version true for intuitionistic propositional logic, and more complicated version for the predicate case.
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  38.  39
    Martin Stokhof (1991). Dynamic Predicate Logic. Linguistics and Philosophy 14 (1):39 - 100.
    This paper is devoted to the formulation and investigation of a dynamic semantic interpretation of the language of first-order predicate logic. The resulting system, which will be referred to as ‘dynamic predicate logic’, is intended as a first step towards a compositional, non-representational theory of discourse semantics.
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  39.  30
    William A. Dembski, Random Predicate Logic I: A Probabilistic Approach to Vagueness.
    Predicates are supposed to slice reality neatly in two halves, one for which the predicate holds, the other for which it fails. Yet far from being razors, predicates tend to be dull knives that mangle reality. If reality is a tomato and predicates are knives, then when these knives divide the tomato, plenty of mush remains unaccounted for. Of course some knives are sharper than others, just as some predicates are less vague than others. “x is water” is certainly (...)
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  40.  11
    Beomin Kim (2008). The Translation of First Order Logic Into Modal Predicate Logic. Proceedings of the Xxii World Congress of Philosophy 13:65-69.
    This paper deals with the translation of first order formulas to predicate S5 formulas. This translation does not bring the first order formula itself to a modal system, but modal interpretation of the first order formula can be given by the translation. Every formula can be translated, and the additional condition such as formula's having only one variable, or having both world domain and individual domain is not required. I introduce an indexical predicate 'E' for the translation. The (...)
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  41. I. I. I. Sem, Dynamic Predicate Logic.
    • 1st try: Free variables in PL (Predicate Logic) (1) Jim1 came in. He1 sat down. (antecedent Jim1 … anaphoric he1) |=M, g cm ιx(x = z1  z1 = jim)  sit z1 iff g(z1) ∈ cm & g(z1) = jim & g(z1) ∈ sit.
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  42.  29
    Bert Mosselmans (2008). Aristotle's Logic and the Quest for the Quantification of the Predicate. Foundations of Science 13 (3-4):195-198.
    This paper examines the quest for the quantification of the predicate, as discussed by W.S. Jevons, and relates it to the discussion about universals and particulars between Plato and Aristotle. We conclude that the quest for the quantification of the predicate can only be achieved by stripping the syllogism from its metaphysical heritage.
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  43.  10
    Herman Dishkant (1986). About Finite Predicate Logic. Studia Logica 45 (4):405 - 414.
    We say that an n-argument predicate P n is finite, if P is a finite set. Note that the set of individuals is infinite! Finite predicates are useful in data bases and in finite mathematics. The logic DBL proposed here operates on finite predicates only. We construct an imbedding for DBL in a special modal logic MPL. We prove that if a finite predicate is expressible in the classical logic, it is also expressible in DBL. Quantifiers are not (...)
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  44. W. V. Quine (1971). Algebraic Logic and Predicate Functors. [Indianapolis,Bobbs-Merrill.
     
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  45.  11
    Petr Hájek, Jeff Paris & John Shepherdson (2000). Rational Pavelka Predicate Logic is a Conservative Extension of Łukasiewicz Predicate Logic. Journal of Symbolic Logic 65 (2):669-682.
    Rational Pavelka logic extends Lukasiewicz infinitely valued logic by adding truth constants r̄ for rationals in [0, 1]. We show that this is a conservative extension. We note that this shows that provability degree can be defined in Lukasiewicz logic. We also give a counterexample to a soundness theorem of Belluce and Chang published in 1963.
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  46.  41
    Ruth Barcan Marcus (2011). C. I. Lewis on Intensional Predicate Logic: A Letter Dated May 11, 1960. History and Philosophy of Logic 32 (2):103 - 106.
    History and Philosophy of Logic, Volume 32, Issue 2, Page 103-106, May 2011.
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  47.  2
    Kai Brünnler (2006). Cut Elimination Inside a Deep Inference System for Classical Predicate Logic. Studia Logica 82 (1):51-71.
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  48.  2
    Dmitrij Skvortsov (2005). On the Predicate Logic of Linear Kripke Frames and Some of its Extensions. Studia Logica 81 (2):261-282.
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  49.  1
    Victor Krivtsov (2010). An Intuitionistic Completeness Theorem for Classical Predicate Logic. Studia Logica 96 (1):109-115.
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  50.  8
    Silvio Ghilardi & Giancarlo Meloni (1996). Relational and Partial Variable Sets and Basic Predicate Logic. Journal of Symbolic Logic 61 (3):843-872.
    In this paper we study the logic of relational and partial variable sets, seen as a generalization of set-valued presheaves, allowing transition functions to be arbitrary relations or arbitrary partial functions. We find that such a logic is the usual intuitionistic and co-intuitionistic first order logic without Beck and Frobenius conditions relative to quantifiers along arbitrary terms. The important case of partial variable sets is axiomatizable by means of the substitutivity schema for equality. Furthermore, completeness, incompleteness and independence results are (...)
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