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  1. added 2020-08-04
    On Classical Set-Compatibility.Luis Felipe Bartolo Alegre - forthcoming - El Jardín de Senderos Que Se Bifurcan y Confluyen.
    In this paper, I generalise the logical concept of compatibility into a broader set-theoretical one. The basic idea is that two sets are incompatible if they produce at least one pair of opposite objects under some operation. I formalise opposition as an operation O: E→E, where E is the set of opposable elements of our universe U, and I propose some models. From this, I define compatibility as a relation C: ℘U × ℘U × ℘U^℘U, which has logical compatibility or (...)
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  2. added 2019-12-07
    A Note on Carnap’s Result and the Connectives.Tristan Haze - 2019 - Axiomathes 29 (3):285-288.
    Carnap’s result about classical proof-theories not ruling out non-normal valuations of propositional logic formulae has seen renewed philosophical interest in recent years. In this note I contribute some considerations which may be helpful in its philosophical assessment. I suggest a vantage point from which to see the way in which classical proof-theories do, at least to a considerable extent, encode the meanings of the connectives (not by determining a range of admissible valuations, but in their own way), and I demonstrate (...)
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  3. added 2019-08-26
    Substitution Structures.Andrew Bacon - 2019 - Journal of Philosophical Logic 48 (6):1017-1075.
    An increasing amount of twenty-first century metaphysics is couched in explicitly hyperintensional terms. A prerequisite of hyperintensional metaphysics is that reality itself be hyperintensional: at the metaphysical level, propositions, properties, operators, and other elements of the type hierarchy, must be more fine-grained than functions from possible worlds to extensions. In this paper I develop, in the setting of type theory, a general framework for reasoning about the granularity of propositions and properties. The theory takes as primitive the notion of a (...)
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  4. added 2019-06-05
    Theories with the Independence Property, Studia Logica 2010 95:379-405.Mlj van de Vel - 2010 - Studia Logica 95 (3):379-405.
    A first-order theory T has the Independence Property provided deduction of a statement of type (quantifiers) (P -> (P1 or P2 or .. or Pn)) in T implies that (quantifiers) (P -> Pi) can be deduced in T for some i, 1 <= i <= n). Variants of this property have been noticed for some time in logic programming and in linear programming. We show that a first-order theory has the Independence Property for the class of basic formulas provided it (...)
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  5. added 2019-03-31
    The Lvov-Warsaw School. Past and Present.Urszula Wybraniec-Skardowska & Ángel Garrido (eds.) - 2018 - Cham, Switzerland: Springer- Birkhauser,.
    This is a collection of new investigations and discoveries on the history of a great tradition, the Lvov-Warsaw School of logic , philosophy and mathematics, by the best specialists from all over the world. The papers range from historical considerations to new philosophical, logical and mathematical developments of this impressive School, including applications to Computer Science, Mathematics, Metalogic, Scientific and Analytic Philosophy, Theory of Models and Linguistics.
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  6. added 2019-03-03
    Laws of Thought and Laws of Logic After Kant.Lydia Patton - 2018 - In Sandra Lapointe (ed.), Logic from Kant to Russell. New York: Routledge. pp. 123-137.
    George Boole emerged from the British tradition of the “New Analytic”, known for the view that the laws of logic are laws of thought. Logicians in the New Analytic tradition were influenced by the work of Immanuel Kant, and by the German logicians Wilhelm Traugott Krug and Wilhelm Esser, among others. In his 1854 work An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities, Boole argues that the laws of thought acquire (...)
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  7. added 2019-02-15
    Syntactic Characterizations of First-Order Structures in Mathematical Fuzzy Logic.Guillermo Badia, Pilar Dellunde, Vicent Costa & Carles Noguera - forthcoming - Soft Computing.
    This paper is a contribution to graded model theory, in the context of mathematical fuzzy logic. We study characterizations of classes of graded structures in terms of the syntactic form of their first-order axiomatization. We focus on classes given by universal and universal-existential sentences. In particular, we prove two amalgamation results using the technique of diagrams in the setting of structures valued on a finite MTL-algebra, from which analogues of the Łoś–Tarski and the Chang–Łoś–Suszko preservation theorems follow.
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  8. added 2018-11-12
    A Statistical Learning Approach to a Problem of Induction.Kino Zhao - manuscript
    At its strongest, Hume's problem of induction denies the existence of any well justified assumptionless inductive inference rule. At the weakest, it challenges our ability to articulate and apply good inductive inference rules. This paper examines an analysis that is closer to the latter camp. It reviews one answer to this problem drawn from the VC theorem in statistical learning theory and argues for its inadequacy. In particular, I show that it cannot be computed, in general, whether we are in (...)
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  9. added 2018-09-20
    The Model-Theoretic Argument: From Skepticism to a New Understanding.Gila Sher - 2016 - In Sanford Goldberg (ed.), The Brain in a Vat. Cambridge, Britain: Cambridge University Press. pp. 208-225.
    In this paper I investigate Putnam’s model-theoretic argument from a transcendent standpoint, in spite of Putnam’s well-known objections to such a standpoint. This transcendence, however, requires ascent to something more like a Tarskian meta-level than what Putnam regards as a “God’s eye view”. Still, it is methodologically quite powerful, leading to a significant increase in our investigative tools. The result is a shift from Putnam’s skeptical conclusion to a new understanding of realism, truth, correspondence, knowledge, and theories, or certain aspects (...)
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  10. added 2018-08-04
    Unexpected Models.Mihail Radu Solcan - 1986 - Revue Roumaine de Philosophie 30 (3-4):211-213.
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  11. added 2018-04-07
    A Model-Theoretic Analysis of Fidel-Structures for mbC.Marcelo E. Coniglio - 2020 - In Can Baskent and Thomas Ferguson (ed.), Graham Priest on Dialetheism and Paraconsistency. Springer. pp. 189-216.
    In this paper the class of Fidel-structures for the paraconsistent logic mbC is studied from the point of view of Model Theory and Category Theory. The basic point is that Fidel-structures for mbC (or mbC-structures) can be seen as first-order structures over the signature of Boolean algebras expanded by two binary predicate symbols N (for negation) and O (for the consistency connective) satisfying certain Horn sentences. This perspective allows us to consider notions and results from Model Theory in order to (...)
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  12. added 2017-12-31
    The Semantics of Entailment.Richard Routley & Robert K. Meyer - 1973 - In Hughes Leblanc (ed.), Truth, Syntax, and Modality: Proceedings Of The Temple University Conference On Alternative Semantlcs. Amsterdam: North-Holland Publishing Company. pp. 199-243.
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  13. added 2017-02-16
    A Methodological Note on Proving Agreement Between the Elementary Process Theory and Modern Interaction Theories.Cabbolet Marcoen - manuscript
    The Elementary Process Theory (EPT) is a collection of seven elementary process-physical principles that describe the individual processes by which interactions have to take place for repulsive gravity to exist. One of the two main problems of the EPT is that there is no proof that the four fundamental interactions (gravitational, electromagnetic, strong, and weak) as we know them can take place in the elementary processes described by the EPT. This paper sets forth the method by which it can be (...)
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  14. added 2017-02-15
    Dispensing with the Generic Sense of" Art'.Raymond Kolcaba - 1989 - Southwest Philosophical Studies 11.
    The question of whether the term ”art,” or art as an array of objects, can be defined depends upon the sense of “art” and its extension. The generic sense of “art” is its broadest meaning having its widest extension. I argue that the term is very much like the generic term “science.” Uses of both terms don’t depend upon rigorous definition. Rather, the terms organize an enormous number of varied and sometimes incompatible sub-categories. Most informative topics in art and science (...)
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  15. added 2017-02-12
    Model-Checking CTL* Over Flat Presburger Counter Systems.Stéphane Demri, Alain Finkel, Valentin Goranko & Govert van Drimmelen - 2010 - Journal of Applied Non-Classical Logics 20 (4):313-344.
    This paper concerns model-checking of fragments and extensions of CTL* on infinite-state Presburger counter systems, where the states are vectors of integers and the transitions are determined by means of relations definable within Presburger arithmetic. In general, reachability properties of counter systems are undecidable, but we have identified a natural class of admissible counter systems (ACS) for which we show that the quantification over paths in CTL* can be simulated by quantification over tuples of natural numbers, eventually allowing translation of (...)
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  16. added 2017-02-12
    Algorithmic Correspondence and Completeness in Modal Logic. IV. Semantic Extensions of SQEMA.Willem Conradie & Valentin Goranko - 2008 - Journal of Applied Non-Classical Logics 18 (2-3):175-211.
    In a previous work we introduced the algorithm \SQEMA\ for computing first-order equivalents and proving canonicity of modal formulae, and thus established a very general correspondence and canonical completeness result. \SQEMA\ is based on transformation rules, the most important of which employs a modal version of a result by Ackermann that enables elimination of an existentially quantified predicate variable in a formula, provided a certain negative polarity condition on that variable is satisfied. In this paper we develop several extensions of (...)
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  17. added 2017-02-09
    Peirce's Omega Point Theory.Eric Steinhart - manuscript
    An Omega Point Theory says that reality is making progress from some initial state to some final state. It moves from some Alpha Point (the initial state) to some Omega Point (the final state). The progress is an increase in some quality. For example, reality is making progress from the chaotic to the orderly; or it is making progress from the simple to the complex; or from the mindless to the mental; or from evil to good. Here we focus on (...)
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  18. added 2017-01-28
    Set Theory.Charles C. Pinter - 1976 - Journal of Symbolic Logic 41 (2):548-549.
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  19. added 2016-10-13
    All Things Must Pass Away.Joshua Spencer - 2012 - Oxford Studies in Metaphysics 7:67.
    Are there any things that are such that any things whatsoever are among them. I argue that there are not. My thesis follows from these three premises: (1) There are two or more things; (2) for any things, there is a unique thing that corresponds to those things; (3) for any two or more things, there are fewer of them than there are pluralities of them.
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  20. added 2015-09-08
    Numerals and Quantifiers in X-Bar Syntax and Their Semantic Interpretation.Henk J. Verkuyl - 1981 - In Jeroen A. G. Groenendijk, Theo M. V. Janssen & Martin B. Stokhof (eds.), Formal Methods in the Study of Language Volume 2. U of Amsterdam. pp. 567-599.
    The first aim of the paper is to show that under certain conditions generative syntax can be made suitable for Montague semantics, based on his type logic. One of the conditions is to make branching in the so-called X-bar syntax strictly binary, This makes it possible to provide an adequate semantics for Noun Phrases by taking them as referring to sets of collections of sets of entities ( type <ett,t>) rather than to sets of sets of entities (ett).
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  21. added 2015-09-08
    Interpretive Rules and the Description of the Aspects.H. J. Verkuyl - 1976 - Foundations of Language 14 (4):471-503.
    This paper aims at showing that the generative-semantic framework is not essential to the proposal in H.J. Verkuyl On the Compositional Nature of the Aspects Reidel:Dordrecht 1972. Compositionality can be shown to be neutral as to the then-difference between generative-semantic and the interpretive-semantic branch of transformational grammar.
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  22. added 2015-08-26
    Constructing Formal Semantics From an Ontological Perspective. The Case of Second-Order Logics.Thibaut Giraud - 2014 - Synthese 191 (10):2115-2145.
    In a first part, I defend that formal semantics can be used as a guide to ontological commitment. Thus, if one endorses an ontological view \(O\) and wants to interpret a formal language \(L\) , a thorough understanding of the relation between semantics and ontology will help us to construct a semantics for \(L\) in such a way that its ontological commitment will be in perfect accordance with \(O\) . Basically, that is what I call constructing formal semantics from an (...)
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  23. added 2015-08-01
    On Pathological Truths.Damian Szmuc & Lucas Rosenblatt - 2014 - Review of Symbolic Logic 7 (4):601-617.
    In Kripke’s classic paper on truth it is argued that by adding a new semantic category different from truth and falsity it is possible to have a language with its own truth predicate. A substantial problem with this approach is that it lacks the expressive resources to characterize those sentences which fall under the new category. The main goal of this paper is to offer a refinement of Kripke’s approach in which this difficulty does not arise. We tackle this characterization (...)
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  24. added 2014-11-07
    A Mathematical Model of Aristotle’s Syllogistic.John Corcoran - 1973 - Archiv für Geschichte der Philosophie 55 (2):191-219.
    In the present article we attempt to show that Aristotle's syllogistic is an underlying logiC which includes a natural deductive system and that it isn't an axiomatic theory as had previously been thought. We construct a mathematical model which reflects certain structural aspects of Aristotle's logic. We examine the relation of the model to the system of logic envisaged in scattered parts of Prior and Posterior Analytics. Our interpretation restores Aristotle's reputation as a logician of consummate imagination and skill. Several (...)
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  25. added 2014-10-28
    Information-Theoretic Logic and Transformation-Theoretic Logic,.John Corcoran - 1999 - In R. A. M. M. (ed.), Fragments in Science,. World Scientific Publishing Company,. pp. 25-35.
    Information-theoretic approaches to formal logic analyze the "common intuitive" concepts of implication, consequence, and validity in terms of information content of propositions and sets of propositions: one given proposition implies a second if the former contains all of the information contained by the latter; one given proposition is a consequence of a second if the latter contains all of the information contained by the former; an argument is valid if the conclusion contains no information beyond that of the premise-set. This (...)
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  26. added 2014-03-08
    Non-Normal Worlds and Representation.Francesco Berto - 2012 - In Michal Peliš & Vít Punčochář (eds.), The Logica Yearbook. College Publications.
    World semantics for relevant logics include so-called non-normal or impossible worlds providing model-theoretic counterexamples to such irrelevant entailments as (A ∧ ¬A) → B, A → (B∨¬B), or A → (B → B). Some well-known views interpret non-normal worlds as information states. If so, they can plausibly model our ability of conceiving or representing logical impossibilities. The phenomenon is explored by combining a formal setting with philosophical discussion. I take Priest’s basic relevant logic N4 and extend it, on the syntactic (...)
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  27. added 2014-03-03
    The Metaphysical Interpretation of Logical Truth.Tuomas Tahko - 2014 - In Penelope Rush (ed.), The Metaphysics of Logic: Logical Realism, Logical Anti-Realism and All Things In Between. Cambridge: Cambridge University Press. pp. 233-248.
    The starting point of this paper concerns the apparent difference between what we might call absolute truth and truth in a model, following Donald Davidson. The notion of absolute truth is the one familiar from Tarski’s T-schema: ‘Snow is white’ is true if and only if snow is white. Instead of being a property of sentences as absolute truth appears to be, truth in a model, that is relative truth, is evaluated in terms of the relation between sentences and models. (...)
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  28. added 2013-06-11
    GENERAL SYSTEM THEORY, LIKEQUANTUM SEMANTICS AND FUZZY SETS.Ignazio Licata - 2006 - In G. Minati (ed.), Systemics of Emergence. Research and Developement. Springer.
    It is outlined the possibility to extend the quantum formalism in relation to the requirements of the general systems theory. It can be done by using a quantum semantics arising from the deep logical structure of quantum theory. It is so possible taking into account the logical openness relationship between observer and system. We are going to show how considering the truth-values of quantum propositions within the context of the fuzzy sets is here more useful for systemics. In conclusion we (...)
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  29. added 2010-11-13
    Non-Classical Metatheory for Non-Classical Logics.Andrew Bacon - 2013 - Journal of Philosophical Logic 42 (2):335-355.
    A number of authors have objected to the application of non-classical logic to problems in philosophy on the basis that these non-classical logics are usually characterised by a classical metatheory. In many cases the problem amounts to more than just a discrepancy; the very phenomena responsible for non-classicality occur in the field of semantics as much as they do elsewhere. The phenomena of higher order vagueness and the revenge liar are just two such examples. The aim of this paper is (...)
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  30. added 2009-04-14
    Categoricity.John Corcoran - 1980 - History and Philosophy of Logic 1 (1):187-207.
    After a short preface, the first of the three sections of this paper is devoted to historical and philosophic aspects of categoricity. The second section is a self-contained exposition, including detailed definitions, of a proof that every mathematical system whose domain is the closure of its set of distinguished individuals under its distinguished functions is categorically characterized by its induction principle together with its true atoms (atomic sentences and negations of atomic sentences). The third section deals with applications especially those (...)
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  31. added 2009-04-07
    Possible M-Diagrams of Models of Arithmetic.Andrew Arana - 2005 - In Stephen Simpson (ed.), Reverse Mathematics 2001.
    In this paper I begin by extending two results of Solovay; the first characterizes the possible Turing degrees of models of True Arithmetic (TA), the complete first-order theory of the standard model of PA, while the second characterizes the possible Turing degrees of arbitrary completions of P. I extend these two results to characterize the possible Turing degrees of m-diagrams of models of TA and of arbitrary complete extensions of PA. I next give a construction showing that the conditions Solovay (...)
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