Jair Minoro Abe (1996)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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In [6] da Costa has introduced a new hierarchy , of logics that are both paraconsistent and paracomplete. Such logics are now known as non-alethic logics. In this article we present an algebraic version of the logics and study some of their properties.
Pavel Pták, John David Maitland Wright (1985)
Aplikace matematiky
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It is shown that for any quantum logic one can find a concrete logic and a surjective homomorphism from onto such that maps the centre of onto the centre of . Moreover, one can ensure that each finite set of compatible elements in is the image of a compatible subset of . This result is “best possible” - let a logic be the homomorphic image of a concrete logic under a homomorphism such that, if is a finite subset of the pre-image of a compatible subset of , then...
John T. Baldwin, Saharon Shelah (2011)
Fundamenta Mathematicae
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Suppose t = (T,T₁,p) is a triple of two countable theories T ⊆ T₁ in vocabularies τ ⊂ τ₁ and a τ₁-type p over the empty set. We show that the Hanf number for the property ’there is a model M₁ of T₁ which omits p, but M₁ ↾ τ is saturated’ is essentially equal to the Löwenheim number of second order logic. In Section 4 we make exact computations of these Hanf numbers and note some distinctions between ’first order’ and ’second order quantification’. In particular, we show that if κ is...
Taneli Huuskonen (2015)
Formalized Mathematics
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This article is the second in a series formalizing some results in my joint work with Prof. Joanna Golinska-Pilarek ([9] and [10]) concerning a logic proposed by Prof. Andrzej Grzegorczyk ([11]). This part presents the syntax and axioms of Grzegorczyk’s Logic of Descriptions (LD) as originally proposed by him, as well as some theorems not depending on any semantic constructions. There are both some clear similarities and fundamental differences between LD and the non-Fregean logics introduced...
Newton C.A. da Costa (1989)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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The Author describes new systems of logic (called "nonalethic") which are both paraconsistent and paracomplete. These systems are connected with the logic of vagueness and with certain philosophical problems (e.g. with some aspects of Hegel's logic).
R. Kulesza (1970)
Applicationes Mathematicae
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Newton C.A. da Costa (1989)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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The Author describes new systems of logic (called "nonalethic") which are both paraconsistent and paracomplete. These systems are connected with the logic of vagueness and with certain philosophical problems (e.g. with some aspects of Hegel's logic).
Slobodan Vujošević (2012)
Review of the National Center for Digitization
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Guido Gherardi, Eugenio Orlandelli (2021)
Bulletin of the Section of Logic
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This paper introduces the logics of super-strict implications, where a super-strict implication is a strengthening of C.I. Lewis' strict implication that avoids not only the paradoxes of material implication but also those of strict implication. The semantics of super-strict implications is obtained by strengthening the (normal) relational semantics for strict implication. We consider all logics of super-strict implications that are based on relational frames for modal logics in the...
Josep Font (1993)
Banach Center Publications
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The aim of this paper is to discuss the motivation for a new general algebraic semantics for deductive systems, to introduce it, and to present an outline of its main features. Some tools from the theory of abstract logics are also introduced, and two classifications of deductive systems are analysed: one is based on the behaviour of the Leibniz congruence (the maximum congruence of a logical matrix) and the other on the behaviour of the Frege operator (which associates to every theory...
T. Traczyk (1964)
Colloquium Mathematicae
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Andrzej Pietruszczak (2017)
Bulletin of the Section of Logic
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This is the first, out of two papers, in which we identify all logics between C1 and S5 having the same theses without iterated modalities. All these logics canbe divided into certain groups. Each such group depends only on which of thefollowing formulas are theses of all logics from this group: (N), (T), (D), ⌜(T)∨ ☐q⌝,and for any n > 0 a formula ⌜(T) ∨ (altn)⌝, where (T) has not the atom ‘q’, and(T) and (altn) have no common atom. We generalize Pollack’s result from [12],where he...
Andrzej Pietruszczak (2017)
Bulletin of the Section of Logic
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This is the second, out of two papers, in which we identify all logics between C1 and S5 having the same theses without iterated modalities. All these logics can be divided into certain groups. Each such group depends only on which of the following formulas are theses of all logics from this group: (N), (T), (D), ⌜(T)∨☐q⌝, and for any n > 0 a formula ⌜(T) ∨ (altn)⌝, where (T) has not the atom ‘q’, and (T) and (altn) have no common atom. We generalize Pollack’s result from [1], where...
Jan Woleński (2009)
Banach Center Publications
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Mitio Takano (2020)
Bulletin of the Section of Logic
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A modified subformula property for the modal logic KD with the additionalaxiom □ ◊(A ∨ B) ⊃ □ ◊ A ∨ □ ◊B is shown. A new modification of the notion of subformula is proposed for this purpose. This modification forms a natural extension of our former one on which modified subformula property for the modal logics K5, K5D and S4.2 has been shown ([2] and [4]). The finite model property as well as decidability for the logic follows from this.