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

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  1.  44
    Andrew Bacon, John Hawthorne & Gabriel Uzquiano (forthcoming). Higher-Order Free Logic and the Prior-Kaplan Paradox. Canadian Journal of Philosophy.
    The principle of Universal Instantiation plays a pivotal role both in the derivation of intensional paradoxes such as Prior's paradox or Kaplan's paradox and the debate between necessitism and contingentism. We outline a distinctively free-logical approach to the intensional paradoxes and note how the free-logical outlook allows one to distinguish two different, though allied themes in higher-order necessitism. We examine the costs of this solution and compare it with the more familiar ramificationist approaches to higher-order logic. Our (...)
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  2.  39
    G. Aldo Antonelli (2000). Proto-Semantics for Positive Free Logic. Journal of Philosophical Logic 29 (3):277-294.
    This paper presents a bivalent extensional semantics for positive free logic without resorting to the philosophically questionable device of using models endowed with a separate domain of "non-existing" objects. The models here introduced have only one (possibly empty) domain, and a partial reference function for the singular terms (that might be undefined at some arguments). Such an approach provides a solution to an open problem put forward by Lambert, and can be viewed as supplying a version of parametrized (...)
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  3.  33
    Karel Lambert (2003). Free Logic: Selected Essays. New Yorkcambridge University Press.
    Free logic is an important field of philosophical logic that first appeared in the 1950s. J. Karel Lambert was one of its founders and coined the term itself. The essays in this collection (written over a period of 40 years) explore the philosophical foundations of free logic and its application to areas as diverse as the philosophy of religion and computer science. Amongst the applications on offer are those to the analysis of existence statements, to (...)
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  4. Dolf Rami, Non‐Standard Neutral Free Logic, Empty Names and Negative Existentials.
    In this paper I am concerned with an analysis of negative existential sentences that contain proper names only by using negative or neutral free logic. I will compare different versions of neutral free logic with the standard system of negative free logic (Burge, Sainsbury) and aim to defend my version of neutral free logic that I have labeled non-standard neutral free logic.
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  5. Karel Lambert (ed.) (1991). Philosophical Applications of Free Logic. Oxford University Press.
    Free logic, an alternative to traditional logic, has been seen as a useful avenue of approach to a number of philosophical issues of contemporary interest. In this collection, Karel Lambert, one of the pioneers in, and the most prominent exponent of, free logic, brings together a variety of published essays bearing on the application of free logic to philosophical topics ranging from set theory and logic to metaphysics and the philosophy of religion. (...)
     
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  6. Dolf Rami, Existence and Free Logic.
    In this paper I aim to defend a first‐order non‐discriminating property view concerning existence. The version of this view that I prefer is based on negative (or a specific neutral) free logic that treats the existence predicate as first‐order logical predicate. I will provide reasons why such a view is more plausible than a second‐order discriminating property view concerning existence and I will also discuss four challenges for the proposed view and provide solutions to them.
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  7.  39
    Norbert Gratzl (2010). A Sequent Calculus for a Negative Free Logic. Studia Logica 96 (3):331-348.
    This article presents a sequent calculus for a negative free logic with identity, called N . The main theorem (in part 1) is the admissibility of the Cut-rule. The second part of this essay is devoted to proofs of soundness, compactness and completeness of N relative to a standard semantics for negative free logic.
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  8.  34
    Maria Lasonen-Aarnio (2008). Why the Externalist is Better Off Without Free Logic: A Reply to McKinsey. Dialectica 62 (4):535-540.
    McKinsey-style incompatibilist arguments attempt to show that the thesis that subjects have privileged, a priori access to the contents of their thoughts is incompatible with semantic externalism. This incompatibility follows – it is urged – from the fact that these theses jointly entail an absurd conclusion, namely, the possibility of a priori knowledge of the world. In a recent paper I argued that a large and important class of such arguments exemplifies a dialectical failure: if they are valid, the putatively (...)
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  9.  5
    Ermanno Bencivenga (2014). Jaśkowski’s Universally Free Logic. Studia Logica 102 (6):1095-1102.
    A universally free logic is a system of quantification theory, with or without identity, whose theses remain logically true if the domain of quantification is empty and some of the singular terms present in the language do not denote existing objects. In the West, logics satisfying and ones satisfying were developed starting in the 1950s. But Stanisław Jaśkowski preceded all this work by some twenty years: his paper “On the Rules of Supposition in Formal Logic” of 1934 (...)
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  10.  4
    Arief Daynes (2006). A New Technique for Proving Realisability and Consistency Theorems Using Finite Paraconsistent Models of Cut‐Free Logic. Mathematical Logic Quarterly 52 (6):540-554.
    A new technique for proving realisability results is presented, and is illustrated in detail for the simple case of arithmetic minus induction. CL is a Gentzen formulation of classical logic. CPQ is CL minus the Cut Rule. The basic proof theory and model theory of CPQ and CL is developed. For the semantics presented CPQ is a paraconsistent logic, i.e. there are non-trivial CPQ models in which some sentences are both true and false. Two systems of arithmetic minus (...)
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  11. Karel Lambert, Alexander Hieke & Edgar Morscher (2001). New Essays in Free Logic in Honour of Karel Lambert. Monograph Collection (Matt - Pseudo).
     
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  12.  27
    Brian Hill & Francesca Poggiolesi (2010). A Contraction-Free and Cut-Free Sequent Calculus for Propositional Dynamic Logic. Studia Logica 94 (1):47 - 72.
    In this paper we present a sequent calculus for propositional dynamic logic built using an enriched version of the tree-hypersequent method and including an infinitary rule for the iteration operator. We prove that this sequent calculus is theoremwise equivalent to the corresponding Hilbert-style system, and that it is contraction-free and cut-free. All results are proved in a purely syntactic way.
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  13.  12
    E. Casanovas, P. Dellunde & R. Jansana (1996). On Elementary Equivalence for Equality-Free Logic. Notre Dame Journal of Formal Logic 37 (3):506-522.
    This paper is a contribution to the study of equality-free logic, that is, first-order logic without equality. We mainly devote ourselves to the study of algebraic characterizations of its relation of elementary equivalence by providing some Keisler-Shelah type ultrapower theorems and an Ehrenfeucht-Fraïssé type theorem. We also give characterizations of elementary classes in equality-free logic. As a by-product we characterize the sentences that are logically equivalent to an equality-free one.
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  14.  29
    Hans-Peter Leeb (2006). State-of-Affairs Semantics for Positive Free Logic. Journal of Philosophical Logic 35 (2):183 - 208.
    In the following the details of a state-of-affairs semantics for positive free logic are worked out, based on the models of common inner domain - outer domain semantics. Lambert's PFL system is proven to be weakly adequate (i.e., sound and complete) with respect to that semantics by demonstrating that the concept of logical truth definable therein coincides with that one of common truth-value semantics for PFL. Furthermore, this state-of-affairs semantics resists the challenges stemming from the slingshot argument since (...)
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  15.  22
    Newton C. A. da Costa & Otavio Bueno (1999). Quasi-Truth, Supervaluations and Free Logic. History and Philosophy of Logic 20 (3-4):215-226.
    The partial structures approach has two major components: a broad notion of structure (partial structure) and a weak notion of truth (quasi-truth). In this paper, we discuss the relationship between this approach and free logic. We also compare the model-theoretic analysis supplied by partial structures with the method of supervaluations, which was initially introduced as a technique to provide a semantic analysis of free logic. We then combine the three formal frameworks (partial structures, free (...) and supervaluations), and apply the resulting approach to accommodate semantic paradoxes. (shrink)
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  16.  18
    Newton C. A. da Costa & Otavio Bueno (1999). Quasi-Truth, Supervaluations and Free Logic. History and Philosophy of Logic 20 (3-4):215-226.
    The partial structures approach has two major components: a broad notion of structure (partial structure) and a weak notion of truth (quasi-truth). In this paper, we discuss the relationship between this approach and free logic. We also compare the model-theoretic analysis supplied by partial structures with the method of supervaluations, which was initially introduced as a technique to provide a semantic analysis of free logic. We then combine the three formal frameworks (partial structures, free (...) and supervaluations), and apply the resulting approach to accommodate semantic paradoxes. (shrink)
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  17. J. Dunn & R. Meyer (1997). Combinators and Structurally Free Logic. Logic Journal of the IGPL 5 (4):505-537.
    A 'Kripke-style' semantics is given for combinatory logic using frames with a ternary accessibility relation, much as in the Tourley-Meyer semantics for relevance logic. We prove by algebraic means a completeness theorem for combinatory logic, by proving a representation theorem for 'combinatory posets.' A philosophical interpretation is given of the models, showing that an element of a combinatory poset can be understood simultaneously as a set of states and as a set of actions on states. This double (...)
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  18.  62
    Karel Lambert (1981). On the Philosophical Foundations of Free Logic. Inquiry 24 (2):147 – 203.
    The essay outlines the character of free logic, and motivation for its construction and development. It details some technical achievements of high philosophical interest, but urges that the role of existence assumptions in logic is still not fully understood, that unresolved old problems, both technical and philosophical, abound, and presents some new problems of considerable philosophical import in free logic.
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  19.  29
    Neil Tennant (2007). Existence and Identity in Free Logic: A Problem for Inferentialism? Mind 116 (464):1055-1078.
    Peter Milne (2007) poses two challenges to the inferential theorist of meaning. This study responds to both. First, it argues that the method of natural deduction idealizes the essential details of correct informal deductive reasoning. Secondly, it explains how rules of inference in free logic can determine unique senses for the existential quantifier and the identity predicate. The final part of the investigation brings out an underlying order in a basic family of free logics.
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  20. R. M. Sainsbury (2006). Facts and Free Logic. ProtoSociology 26:119–27.
    Comment on S. Neale's, "Facts and Free Logic".
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  21.  33
    Cristina Coppola, Giangiacomo Gerla & Annamaria Miranda (2010). Point-Free Foundation of Geometry and Multivalued Logic. Notre Dame Journal of Formal Logic 51 (3):383-405.
    Whitehead, in two basic books, considers two different approaches to point-free geometry: the inclusion-based approach , whose primitive notions are regions and inclusion relation between regions, and the connection-based approach , where the connection relation is considered instead of the inclusion. We show that the latter cannot be reduced to the first one, although this can be done in the framework of multivalued logics.
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  22.  28
    Peter Milne (2007). Existence and Identity in Free Logic: Two Comments. Mind 116 (464):1079-1082.
    Professor Tennant and I agree on much regarding the proof-theoretic semantics of free logic. Here I point to two issues, one on which we disagree, the other on which I find it hard to say how closely we may agree. The first concerns the exact content of Tennant's Rule of Atomic Denotation. The second concerns the nature of assumptions whose formal counterparts contain parametric occurrences of names.
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  23. Karel Lambert (2005). Free Logic: Selected Essays. Cambridge University Press.
    Free logic is an important field of philosophical logic that first appeared in the 1950s. J. Karel Lambert was one of its founders and coined the term itself. The essays in this collection explore the philosophical foundations of free logic and its application to areas as diverse as the philosophy of religion and computer science. Amongst the applications on offer are those to the analysis of existence statements, to definite descriptions and to partial functions. The (...)
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  24. Karel Lambert (2007). Free Logic: Selected Essays. Cambridge University Press.
    Free logic is an important field of philosophical logic that first appeared in the 1950s. J. Karel Lambert was one of its founders and coined the term itself. The essays in this collection explore the philosophical foundations of free logic and its application to areas as diverse as the philosophy of religion and computer science. Amongst the applications on offer are those to the analysis of existence statements, to definite descriptions and to partial functions. The (...)
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  25. Karel Lambert (2012). Free Logic: Selected Essays. Cambridge University Press.
    Free logic is an important field of philosophical logic that first appeared in the 1950s. J. Karel Lambert was one of its founders and coined the term itself. The essays in this collection explore the philosophical foundations of free logic and its application to areas as diverse as the philosophy of religion and computer science. Amongst the applications on offer are those to the analysis of existence statements, to definite descriptions and to partial functions. The (...)
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  26.  13
    Francesco Orilia (1994). Belief Representation in a Deductivist Type-Free Doxastic Logic. Minds and Machines 4 (2):163-203.
    Konolige''s technical notion of belief based on deduction structures is briefly reviewed and its usefulness for the design of artificial agents with limited representational and deductive capacities is pointed out. The design of artificial agents with more sophisticated representational and deductive capacities is then taken into account. Extended representational capacities require in the first place a solution to the intensional context problems. As an alternative to Konolige''s modal first-order language, an approach based on type-free property theory is proposed. It (...)
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  27.  6
    Kenneth A. Bowen (1980). Interpolation in Loop-Free Logic. Studia Logica 39 (2-3):297 - 310.
    Model-theoretic methods are used to extend Craig's Interpolation Theorem to the loop-free portion of Pratt's dynamic logic of programs with simple assignments.
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  28.  17
    Peter van Inwagen (1990). Logic and the Free Will Problem. Social Theory and Practice 16 (3):277-90.
  29. K. Bimbó & J. Dunn (1998). Two Extensions of the Structurally Free Logic LC. Logic Journal of the Igpl 6 (3):403-424.
    The paper considers certain extensions of the system LC introduced in Dunn & Meyer 1997. LC is a structurally free system , but it has combinators as formulas in the place of structural rules. We consider two ways to extend LC with conjunction and disjunction depending on whether they distribute over each other or not. We prove the elimination theorem for the systems. At the end of the paper we give a Routley-Meyer style semantics for the distributive extension, including (...)
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  30.  5
    Theodore Hailperin (1992). Herbrand Semantics, the Potential Infinite, and Ontology-Free Logic. History and Philosophy of Logic 13 (1):69-90.
    This paper investigates the ontological presuppositions of quantifier logic. It is seen that the actual infinite, although present in the usual completeness proofs, is not needed for a proper semantic foundation. Additionally, quantifier logic can be given an adequate formulation in which neither the notion of individual nor that of a predicate appears.
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  31.  2
    Norbert Gratzl (2010). A Sequent Calculus for a Negative Free Logic. Studia Logica 96 (3):331-348.
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  32.  18
    M. Randall Holmes (2003). Karel Lambert, Free Logic: Selected Essays. Studia Logica 75 (3):413-419.
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  33.  10
    Colin R. Caret & Zach Weber (2015). A Note on Contraction-Free Logic for Validity. Topoi 34 (1):63-74.
    This note motivates a logic for a theory that can express its own notion of logical consequence—a ‘syntactically closed’ theory of naive validity. The main issue for such a logic is Curry’s paradox, which is averted by the failure of contraction. The logic features two related, but different, implication connectives. A Hilbert system is proposed that is complete and non-trivial.
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  34.  22
    Jarmo Kontinen (2013). Coherence and Computational Complexity of Quantifier-Free Dependence Logic Formulas. Studia Logica 101 (2):267-291.
    We study the computational complexity of the model checking problem for quantifier-free dependence logic ${(\mathcal{D})}$ formulas. We characterize three thresholds in the complexity: logarithmic space (LOGSPACE), non-deterministic logarithmic space (NL) and non-deterministic polynomial time (NP).
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  35.  34
    Robert K. Meyer & Karel Lambert (1968). Universally Free Logic and Standard Quantification Theory. Journal of Symbolic Logic 33 (1):8-26.
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  36.  14
    Peter W. Woodruff (1984). On Supervaluations in Free Logic. Journal of Symbolic Logic 49 (3):943-950.
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  37.  41
    Scott Lehmann (1994). Strict Fregean Free Logic. Journal of Philosophical Logic 23 (3):307--336.
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  38.  31
    Karel Lambert (1967). Free Logic and the Concept of Existence. Notre Dame Journal of Formal Logic 8 (1-2):133-144.
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  39.  51
    Ermanno Bencivenga (1976). Set Theory and Free Logic. Journal of Philosophical Logic 5 (1):1 - 15.
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  40.  56
    Roy Dyckhoff & Luis Pinto (1998). Cut-Elimination and a Permutation-Free Sequent Calculus for Intuitionistic Logic. Studia Logica 60 (1):107-118.
    We describe a sequent calculus, based on work of Herbelin, of which the cut-free derivations are in 1-1 correspondence with the normal natural deduction proofs of intuitionistic logic. We present a simple proof of Herbelin's strong cut-elimination theorem for the calculus, using the recursive path ordering theorem of Dershowitz.
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  41.  16
    Karel Lambert & Ermanno Bencivenga (1986). A Free Logic with Simple and Complex Predicates. Notre Dame Journal of Formal Logic 27 (2):247-256.
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  42.  5
    Ermanno Bencivenga (1984). A Possibility-Free Logic of Descriptions. Archive for Mathematical Logic 24 (1):159-165.
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  43.  18
    Richard L. Mendelsohn (1989). Objects and Existence: Reflections on Free Logic. Notre Dame Journal of Formal Logic 30 (4):604-623.
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  44.  1
    Raymond D. Gumb (1979). An Extended Joint Consistency Theorem for Free Logic with Equality. Notre Dame Journal of Formal Logic 20 (2):321-335.
  45.  7
    Bas C. van Fraassen (1968). A Topological Proof of the Löwenheim‐Skolem, Compactness, and Strong Completeness Theorems for Free Logic. Mathematical Logic Quarterly 14 (13‐17):245-254.
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  46. Peter Simons (1985). Lesniewski's Logic and its Relation to Classical and Free Logic. In G. Dorn & P. Weingarten (eds.), Foundations of Logic and Linguistics. Problems and Solutions. Plenum 369-400.
     
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  47.  11
    Ermanno Bencivenga (1978). A Semantics for a Weak Free Logic. Notre Dame Journal of Formal Logic 19 (4):646-652.
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  48.  10
    Ermanno Bencivenga (1980). A Weak Free Logic with the Existence Sign. Notre Dame Journal of Formal Logic 21 (3):572-576.
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  49.  8
    Henri J. Sarlet (1977). Hintikka's Free Logic is Not Free. Notre Dame Journal of Formal Logic 18 (3):458-458.
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  50.  7
    Kathleen Johnson Wu (1988). A Basic Free Logic. Notre Dame Journal of Formal Logic 29 (4):543-552.
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