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  1. Alexander Abian (1972). Categoricity of Denumerable Atomless Boolean Rings. Studia Logica 30 (1):63 - 68.
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  2. Jarosław Achinger (1986). On a Problem of P(Α, Δ, Π) Concerning Generalized Alexandroff S Cube. Studia Logica 45 (3):293 - 300.
    Universality of generalized Alexandroff's cube plays essential role in theory of absolute retracts for the category of , -closure spaces. Alexandroff's cube. is an , -closure space generated by the family of all complete filters. in a lattice of all subsets of a set of power .Condition P(, , ) says that is a closure space of all , -filters in the lattice ( ).
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  3. O. M. Anshakov, D. V. Vinogradov & V. K. Finn (eds.) (2008). Mnogoznachnye Logiki I Ikh Primenenii͡a. Lki.
    Tom 1. Logicheskie ischisleni͡a, algebry i funkt͡sionalnye svoĭstva.
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  4. Bradley Armour-Garb & James A. Woodbridge (2010). Truthmakers, Paradox and Plausibility. Analysis 70 (1):11-23.
    In a series of articles, Dan Lopez De Sa and Elia Zardini argue that several theorists have recently employed instances of paradoxical reasoning, while failing to see its problematic nature because it does not immediately (or obviously) yield inconsistency. In contrast, Lopez De Sa and Zardini claim that resultant inconsistency is not a necessary condition for paradoxicality. It is our contention that, even given their broader understanding of paradox, their arguments fail to undermine the instances of reasoning they attack, either (...)
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  5. Jon Barwise (1975). Admissible Sets and Structures: An Approach to Definability Theory. Springer-Verlag.
  6. Ali Behboud (2006). Steve Russ. The Mathematical Works of Bernard Bolzano. Oxford: Oxford University Press, 2004. Pp. XXX + 698. Isbn 0-19-853930-. [REVIEW] Philosophia Mathematica 14 (3):352-362.
  7. Giacomo Bonanno (1999). Synchronic Information, Knowledge and Common Knowledge in Extensive Games. Research in Economics 53 (1):77-99.
    Restricting attention to the class of extensive games defined by von Neumann and Morgenstern with the added assumption of perfect recall, we specify the information of each player at each node of the game-tree in a way which is coherent with the original information structure of the extensive form. We show that this approach provides a framework for a formal and rigorous treatment of questions of knowledge and common knowledge at every node of the tree. We construct a particular information (...)
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  8. Roy T. Cook (2002). Vagueness and Mathematical Precision. Mind 111 (442):225-247.
    One of the main reasons for providing formal semantics for languages is that the mathematical precision afforded by such semantics allows us to study and manipulate the formalization much more easily than if we were to study the relevant natural languages directly. Michael Tye and R. M. Sainsbury have argued that traditional set-theoretic semantics for vague languages are all but useless, however, since this mathematical precision eliminates the very phenomenon (vagueness) that we are trying to capture. Here we meet this (...)
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  9. Haskell B. Curry (1963/1977). Foundations of Mathematical Logic. Dover Publications.
    Comprehensive account of constructive theory of first-order predicate calculus. Covers formal methods including algorithms and epi-theory, brief treatment of Markov’s approach to algorithms, elementary facts about lattices and similar algebraic systems, more. Philosophical and reflective as well as mathematical. Graduate-level course. 1963 ed. Exercises.
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  10. Costas Dimitracopoulos (ed.) (2008). Logic Colloquium 2005: Proceedings of the Annual European Summer Meeting of the Association for Symbolic Logic, Held in Athens, Greece, July 28-August 3, 2005. [REVIEW] Cambridge University Press.
    The Annual European Meeting of the Association for Symbolic Logic, generally known as the Logic Colloquium, is the most prestigious annual meeting in the field. Many of the papers presented there are invited surveys of recent developments. Highlights of this volume from the 2005 meeting include three papers on different aspects of connections between model theory and algebra; a survey of recent major advances in combinatorial set theory; a tutorial on proof theory and modal logic; and a description of Bernay's (...)
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  11. Roy Dowsing (1986). A First Course in Formal Logic and its Applications in Computer Science. Blackwell Scientific Publications.
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  12. Federico Faroldi (2013). Verità d'imperativi in Kalle Sorainen. Rivista Internazionale di Filosofia Del Diritto 90 (1):93–98.
    This brief note explores Sorainen's (1939) contribution to the birth of deontic logic. He maintained that imperatives can be true or, respectively, false.
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  13. Joanna Golińska-Pilarek & Taneli Huuskonen (2012). Logic. Of Descriptions. A New Approach to the Foundations of Mathematics and Science. Studies in Logic, Grammar and Rhetoric 27:63-94.
    We study a new formal logic LD introduced by Prof. Grzegorczyk. The logic is based on so-called descriptive equivalence, corresponding to the idea of shared meaning rather than shared truth value. We construct a semantics for LD based on a new type of algebras and prove its soundness and complete- ness. We further show several examples of classical laws that hold for LD as well as laws that fail. Finally, we list a number of open problems.
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  14. Harold T. Hodes (1989). Three Value Logics: An Introduction, A Comparison of Various Logical Lexica and Some Philosophical Remarks. Annals of Pure and Applied Logic 43 (2):99-145.
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  15. Luca Incurvati & Julien Murzi (2008). How Basic is the Basic Revisionary Argument? Analysis 68 (4):303-309.
    Anti-realists typically contend that truth is epistemically constrained. Truth, they say, cannot outstrip our capacity to know. Some anti-realists are also willing to make a further claim: if truth is epistemically constrained, classical logic is to be given up in favour of intuitionistic logic. Here we shall be concerned with one argument in support of this thesis - Crispin Wright's Basic Revisionary Argument, first presented in his Truth and Objectivity. We argue that the reasoning involved in the argument, if correct, (...)
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  16. Nicholas Joll (2010). Theories of Judgment: Psychology, Logic, Phenomenology – Wayne M. Martin. Philosophical Quarterly 60 (240):658-660.
  17. Joke Meheus & Dagmar Provijn (2007). Abduction Through Semantic Tableaux Versus Abduction Through Goal-Directed Proofs. Theoria 22 (3):295-304.
    In this paper, we present a goal-directed proof procedure for abductive reasoning. This procedure will be compared with Aliseda’s approach based on semantic tableaux. We begin with some comments on Aliseda’s algorithms for computing conjunctive abductions and show that they do not entirely live up to their aims. Next we give a concise account of goal-directed proofs and we show that abductive explanations are a natural spin-off of these proofs. Finally, we show that the goal-directed procedure solves the problems we (...)
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  18. Michael Nelson & Edward N. Zalta (2012). A Defense of Contingent Logical Truths. Philosophical Studies 157 (1):153-162.
    A formula is a contingent logical truth when it is true in every model M but, for some model M , false at some world of M . We argue that there are such truths, given the logic of actuality. Our argument turns on defending Tarski’s definition of truth and logical truth, extended so as to apply to modal languages with an actuality operator. We argue that this extension is the philosophically proper account of validity. We counter recent arguments to (...)
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  19. Ángel Nepomuceno-Fernández & Fernando Soler-Toscano (2007). Metamodeling Abduction. Theoria 22 (3):285-293.
    Abduction can be intended as a special kind of deductive consequence. In fact a general trend is to consider it as a backward deduction with some additional conditions. However, there can be more than one kind of deduction, so that any definition of abduction must take that into account. From a logical perspec-tive the problem is precisely the formalization of conditions when the deductive consequence is fixed. In this paper, we adopt Makinson’s method to define new consequence relations, hence abduction (...)
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  20. Ilkka Niiniluoto (2007). Structural Rules for Abduction. Theoria 22 (3):325-329.
    Atocha Aliseda’s Abductive Reasoning (2006) gives a structural characterization of the “forward” explana-tory reasoning from a theory to observational data. This paper asks whether there are any interesting structural rules for the “backward” abductive reasoning from observations to explanatory theories. Ignoring statistical cases, a partial explication of abduction is converse deductive explanation: h is abducible from e iff h deductively explains e. This relation of abducibility trivially satisfies Converse Entailment (if h entails e, then h is abducible from e ), (...)
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  21. Paul Oppenheimer & Edward N. Zalta (2011). Relations Vs Functions at the Foundations of Logic: Type-Theoretic Considerations. Journal of Logic and Computation 21:351-374.
    Though Frege was interested primarily in reducing mathematics to logic, he succeeded in reducing an important part of logic to mathematics by defining relations in terms of functions. By contrast, Whitehead & Russell reduced an important part of mathematics to logic by defining functions in terms of relations (using the definite description operator). We argue that there is a reason to prefer Whitehead & Russell's reduction of functions to relations over Frege's reduction of relations to functions. There is an interesting (...)
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  22. Stathos Psillos (2002). Computational Logic: Logic Programming and Beyond : Essays in Honour of Robert A. Kowalski, Part Ii. Springer Berlin.
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  23. Roberto Rojo (1957). La posibilidad de una lógica vital en Ortega / The Possibility of a Vital Logic in Ortega. Humanitas 3 (8):151-153.
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  24. Helge Rückert, Dialogues as a Dynamic Framework for Logic.
    Dialogical logic is a game-theoretical approach to logic. Logic is studied with the help of certain games, which can be thought of as idealized argumentations. Two players, the Proponent, who puts forward the initial thesis and tries to defend it, and the Opponent, who tries to attack the Proponent’s thesis, alternately utter argumentative moves according to certain rules. For a long time the dialogical approach had been worked out only for classical and intuitionistic logic. The seven papers of this (...)
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  25. Stewart Shapiro (1980). On the Notion of Effectiveness. History and Philosophy of Logic 1 (1-2):209-230.
    This paper focuses on two notions of effectiveness which are not treated in detail elsewhere. Unlike the standard computability notion, which is a property of functions themselves, both notions of effectiveness are properties of interpreted linguistic presentations of functions. It is shown that effectiveness is epistemically at least as basic as computability in the sense that decisions about computability normally involve judgments concerning effectiveness. There are many occurrences of the present notions in the writings of logicians; moreover, consideration of these (...)
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  26. Gregory Wheeler & Pedro Barahona (2012). Why the Hardest Logic Puzzle Ever Cannot Be Solved in Less Than Three Questions. Journal of Philosophical Logic 41 (2):493-503.
    Rabern and Rabern (Analysis 68:105–112 2 ) and Uzquiano (Analysis 70:39–44 4 ) have each presented increasingly harder versions of ‘the hardest logic puzzle ever’ (Boolos The Harvard Review of Philosophy 6:62–65 1 ), and each has provided a two-question solution to his predecessor’s puzzle. But Uzquiano’s puzzle is different from the original and different from Rabern and Rabern’s in at least one important respect: it cannot be solved in less than three questions. In this paper we solve Uzquiano’s puzzle (...)
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  27. John Woods (2007). Ignorance and Semantic Tableaux: Aliseda on Abduction. Theoria 22 (3):305-318.
    This is an examination of similarities and differences between two recent models of abductive reasoning. The one is developed in Atocha Aliseda’s Abductive Reasoning: Logical Investigations into the Processes of Discovery and Evaluation (2006). The other is advanced by Dov Gabbay and the present author in their The Reach of Abduction: Insight and Trial (2005). A principal difference between the two approaches is that in the Gabbay-Woods model, but not in the Aliseda model, abductive inference is ignorance-preserving. A further differ-ence (...)
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Dialetheism
  1. Sam Alxatib, Peter Pagin & Uli Sauerland (2013). Acceptable Contradictions: Pragmatics or Semantics? A Reply to Cobreros Et Al. [REVIEW] Journal of Philosophical Logic 42 (4):619-634.
    Naive speakers find some logical contradictions acceptable, specifically borderline contradictions involving vague predicates such as Joe is and isn’t tall. In a recent paper, Cobreros et al. (J Philos Logic, 2012) suggest a pragmatic account of the acceptability of borderline contradictions. We show, however, that the pragmatic account predicts the wrong truth conditions for some examples with disjunction. As a remedy, we propose a semantic analysis instead. The analysis is close to a variant of fuzzy logic, but conjunction and disjunction (...)
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  2. Sam Alxatib & Francis Jeffry Pelletier (2011). The Psychology of Vagueness: Borderline Cases and Contradictions. Mind and Language 26 (3):287-326.
    In an interesting experimental study, Bonini et al. (1999) present partial support for truth-gap theories of vagueness. We say this despite their claim to find theoretical and empirical reasons to dismiss gap theories and despite the fact that they favor an alternative, epistemic account, which they call ‘vagueness as ignorance’. We present yet more experimental evidence that supports gap theories, and argue for a semantic/pragmatic alternative that unifies the gappy supervaluationary approach together with its glutty relative, the subvaluationary approach.
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  3. C. M. Amus (2012). Paraconsistency on the Rocks of Dialetheism. Logique Et Analyse 55 (217):3.
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  4. Constantin Antonopoulos (1993). 'Neither-Nor' Statements and 'Neither-Nor' States. History and Philosophy of Logic 14 (2):183-199.
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  5. O. Arieli, A. Avron & A. Zamansky (2011). Ideal Paraconsistent Logics. Studia Logica 99 (1-3):31-60.
    We define in precise terms the basic properties that an ‘ideal propositional paraconsistent logic’ is expected to have, and investigate the relations between them. This leads to a precise characterization of ideal propositional paraconsistent logics. We show that every three-valued paraconsistent logic which is contained in classical logic, and has a proper implication connective, is ideal. Then we show that for every n > 2 there exists an extensive family of ideal n -valued logics, each one of which is not (...)
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  6. B. Armour-Garb (2012). No Consistent Way with Paradox. Analysis 72 (1):66-75.
    In ‘A Consistent Way with Paradox’, Laurence Goldstein (2009) clarifies his solution to the liar, which he touts as revenge immune . In addition, he (Ibid.) responds to one of the objections that Armour-Garb and Woodbridge (2006) raise against certain solutions to the open pair and argues that his proffered solution to the liar family of paradoxes undermines what they (Ibid.) call the dialetheic conjecture . In this paper, after critically evaluating Goldstein’s response to A-G&W, I turn to his proposed (...)
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  7. Bradley Armour-Garb (2005). Wrestling with (and Without) Dialetheism. Australasian Journal of Philosophy 83 (1):87 – 102.
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  8. Bradley Armour-Garb & J. C. Beall (2001). Can Deflationists Be Dialetheists? Journal of Philosophical Logic 30 (6):593-608.
    Philosophical work on truth covers two streams of inquiry, one concerning the nature (if any) of truth, the other concerning truth-related paradox, especially the Liar. For the most part these streams have proceeded fairly independently of each other. In his "Deflationary Truth and the Liar" (JPL 28:455-488, 1999) Keith Simmons argues that the two streams bear on one another in an important way; specifically, the Liar poses a greater problem for deflationary conceptions of truth than it does for inflationist conceptions. (...)
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  9. Bradley Armour-Garb & James A. Woodbridge (2012). Liars, Truthtellers and Naysayers: A Broader View of Semantic Pathology I. Language and Communication 32 (4):293-311.
    Semantic pathology is most widely recognized in the liar paradox, where an apparent inconsistency arises in ‘‘liar sentences’’ and their ilk. But the phenomenon of semantic pathology also manifests a sibling symptom—an apparent indeterminacy—which, while not largely discussed (save for the occasional nod to ‘‘truthteller sentences’’), is just as pervasive as, and exactly parallels, the symptom of inconsistency. Moreover, certain ‘‘dual symptom’’ cases, which we call naysayers, exhibit both inconsistency and indeterminacy and also manifest a higher-order indeterminacy between them. In (...)
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  10. Bradley Armour-Garb & James A. Woodbridge (2006). Dialetheism, Semantic Pathology, and the Open Pair. Australasian Journal of Philosophy 84 (3):395 – 416.
    Over the past 25 years, Graham Priest has ably presented and defended dialetheism, the view that certain sentences are properly characterized as true with true negations. Our goal here is neither to quibble with the tenability of true, assertable contradictions nor, really, with the arguments for dialetheism. Rather, we wish to address the dialetheist's treatment of cases of semantic pathology and to pose a worry for dialetheism that has not been adequately considered. The problem that we present seems to have (...)
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  11. Bradley Armour-Garb & James A. Woodbridge (2003). Curried Katz with Epimenidean Dilemma. Philosophical Forum 34 (3-4):351-366.
  12. Jack Arnold & Stewart Shapiro (2007). Where in the (World Wide) Web of Belief is the Law of Non-Contradiction? Noûs 41 (2):276–297.
    It is sometimes said that there are two, competing versions of W. V. O. Quine’s unrelenting empiricism, perhaps divided according to temporal periods of his career. According to one, logic is exempt from, or lies outside the scope of, the attack on the analytic-synthetic distinction. This logic-friendly Quine holds that logical truths and, presumably, logical inferences are analytic in the traditional sense. Logical truths are knowable a priori, and, importantly, they are incorrigible, and so immune from revision. The other, radical (...)
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  13. J. C. Beall (2009). Spandrels of Truth. Oxford University Press.
    In Spandrels of Truth, Beall concisely presents and defends a modest, so-called dialetheic theory of transparent truth.
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  14. Jc Beall (2012). Future Contradictions. Australasian Journal of Philosophy 90 (3):547-557.
    A common and much-explored thought is ?ukasiewicz's idea that the future is ?indeterminate??i.e., ?gappy? with respect to some claims?and that such indeterminacy bleeds back into the present in the form of gappy ?future contingent? claims. What is uncommon, and to my knowledge unexplored, is the dual idea of an overdeterminate future?one which is ?glutty? with respect to some claims. While the direct dual, with future gluts bleeding back into the present, is worth noting, my central aim is simply to sketch (...)
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  15. JC Beall & Bradley Armour-Garb (2003). Should Deflationists Be Dialetheists? Noûs 37 (2):303–324.
  16. Jc Beall & David Ripley (2004). Analetheism and Dialetheism. Analysis 64 (281):30–35.
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  17. Francesco Berto (2014). Absolute Contradiction, Dialetheism, and Revenge. Review of Symbolic Logic 7 (2):193-207.
    Is there a notion of contradiction—let us call it, for dramatic effect, “absolute”—making all contradictions, so understood, unacceptable also for dialetheists? It is argued in this paper that there is, and that spelling it out brings some theoretical benefits. First it gives us a foothold on undisputed ground in the methodologically difficult debate on dialetheism. Second, we can use it to express, without begging questions, the disagreement between dialetheists and their rivals on the nature of truth. Third, dialetheism has an (...)
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  18. Francesco Berto (2008). Adynaton and Material Exclusion. Australasian Journal of Philosophy 86 (2):165 – 190.
    Philosophical dialetheism, whose main exponent is Graham Priest, claims that some contradictions hold, are true, and it is rational to accept and assert them. Such a position is naturally portrayed as a challenge to the Law of Non-Contradiction (LNC). But all the classic formulations of the LNC are, in a sense, not questioned by a typical dialetheist, since she is (cheerfully) required to accept them by her own theory. The goal of this paper is to develop a formulation of the (...)
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  19. Francesco Berto (2007). How to Sell a Contradiction. College Publications.
    There is a principle in things, about which we cannot be deceived, but must always, on the contrary, recognize the truth – viz. that the same thing cannot at one and the same time be and not be": with these words of the Metaphysics, Aristotle introduced the Law of Non-Contradiction, which was to become the most authoritative principle in the history of Western thought. However, things have recently changed, and nowadays various philosophers, called dialetheists, claim that this Law does not (...)
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  20. Francesco Berto (2007). Is Dialetheism an Idealism? The Russellian Fallacy and the Dialetheist's Dilemma. Dialectica 61 (2):235–263.
    In his famous work on vagueness, Russell named “fallacy of verbalism” the fallacy that consists in mistaking the properties of words for the properties of things. In this paper, I examine two (clusters of) mainstream paraconsistent logical theories – the non-adjunctive and relevant approaches –, and show that, if they are given a strongly paraconsistent or dialetheic reading, the charge of committing the Russellian Fallacy can be raised against them in a sophisticated way, by appealing to the intuitive reading of (...)
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  21. Francesco Berto (2006). Characterizing Negation to Face Dialetheism. Logique Et Analyse 49 (195):241-263.
  22. Francesco Berto (2006). Meaning, Metaphysics, and Contradiction. American Philosophical Quarterly 43 (4):283-297.
  23. Francesco Berto (2006). Teorie Dell'assurdo: I Rivali Del Principio di Non-Contraddizione. Carocci.
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