排序方式: 共有193条查询结果,搜索用时 15 毫秒
91.
Elia Zardini 《Studia Logica》2008,90(3):337-368
According to the naive theory of vagueness, the vagueness of an expression consists in the existence of both positive and
negative cases of application of the expression and in the non-existence of a sharp cut-off point between them. The sorites
paradox shows the naive theory to be inconsistent in most logics proposed for a vague language. The paper explores the prospects
of saving the naive theory by revising the logic in a novel way, placing principled restrictions on the transitivity of the
consequence relation. A lattice-theoretical framework for a whole family of (zeroth-order) “tolerant logics” is proposed and
developed. Particular care is devoted to the relation between the salient features of the formal apparatus and the informal
logical and semantic notions they are supposed to model. A suitable non-transitive counterpart to classical logic is defined.
Some of its properties are studied, and it is eventually shown how an appropriate regimentation of the naive theory of vagueness
is consistent in such a logic. 相似文献
92.
Algebraic Aspects of Cut Elimination 总被引:2,自引:2,他引:0
We will give here a purely algebraic proof of the cut elimination theorem for various sequent systems. Our basic idea is to introduce mathematical structures, called Gentzen structures, for a given sequent system without cut, and then to show the completeness of the sequent system without cut with respect to the class of algebras for the sequent system with cut, by using the quasi-completion of these Gentzen structures. It is shown that the quasi-completion is a generalization of the MacNeille completion. Moreover, the finite model property is obtained for many cases, by modifying our completeness proof. This is an algebraic presentation of the proof of the finite model property discussed by Lafont [12] and Okada-Terui [17]. 相似文献
93.
This paper concerns a (prospective) goal directed proof procedure for the propositional fragment of the inconsistency-adaptive logic ACLuN1. At the propositional level, the procedure forms an algorithm for final derivability. If extended to the predicative level, it provides a criterion for final derivability. This is essential in view of the absence of a positive test. The procedure may be generalized to all flat adaptive logics. 相似文献
94.
Paraconsistent logic from a modal viewpoint 总被引:1,自引:0,他引:1
Jean-Yves Bziau 《Journal of Applied Logic》2005,3(1):7-14
In this paper we study paraconsistent negation as a modal operator, considering the fact that the classical negation of necessity has a paraconsistent behavior. We examine this operator on the one hand in the modal logic S5 and on the other hand in some new four-valued modal logics. 相似文献
95.
Arnon Avron 《Studia Logica》2005,80(2-3):159-194
We investigate two large families of logics, differing from each other by the treatment of negation. The logics in one of
them are obtained from the positive fragment of classical logic (with or without a propositional constant ff for “the false”)
by adding various standard Gentzen-type rules for negation. The logics in the other family are similarly obtained from LJ+, the positive fragment of intuitionistic logic (again, with or without ff). For all the systems, we provide simple semantics
which is based on non-deterministic four-valued or three-valued structures, and prove soundness and completeness for all of
them. We show that the role of each rule is to reduce the degree of non-determinism in the corresponding systems. We also
show that all the systems considered are decidable, and our semantics can be used for the corresponding decision procedures.
Most of the extensions of LJ+ (with or without ff) are shown to be conservative over the underlying logic, and it is determined which of them are not. 相似文献
96.
Dimiter Vakarelov 《Studia Logica》2005,80(2-3):393-430
Constructive logic with Nelson negation is an extension of the intuitionistic logic with a special type of negation expressing some features of constructive falsity and refutation by counterexample. In this paper we generalize this logic weakening maximally the underlying intuitionistic negation. The resulting system, called subminimal logic with Nelson negation, is studied by means of a kind of algebras called generalized N-lattices. We show that generalized N-lattices admit representation formalizing the intuitive idea of refutation by means of counterexamples giving in this way a counterexample semantics of the logic in question and some of its natural extensions. Among the extensions which are near to the intuitionistic logic are the minimal logic with Nelson negation which is an extension of the Johansson's minimal logic with Nelson negation and its in a sense dual version — the co-minimal logic with Nelson negation. Among the extensions near to the classical logic are the well known 3-valued logic of Lukasiewicz, two 12-valued logics and one 48-valued logic. Standard questions for all these logics — decidability, Kripke-style semantics, complete axiomatizability, conservativeness are studied. At the end of the paper extensions based on a new connective of self-dual conjunction and an analog of the Lukasiewicz middle value ½ have also been considered. 相似文献
97.
Sergei P. Odintsov 《Studia Logica》2005,80(2-3):291-320
The article is devoted to the systematic study of the lattice εN4⊥ consisting of logics extending N4⊥. The logic N4⊥ is obtained from paraconsistent Nelson logic N4 by adding the new constant ⊥ and axioms ⊥ → p, p → ∼ ⊥. We study interrelations between εN4⊥ and the lattice of superintuitionistic logics. Distinguish in εN4⊥ basic subclasses of explosive logics, normal logics, logics of general form and study how they are relate.
The author acknowledges support by the Alexander von Humboldt-Stiftung and by Counsil for Grants under RF President, project
NSh - 2112.2003.1. 相似文献
98.
Joke Meheus 《Journal of Philosophical Logic》2006,35(6):539-567
In this paper, I present the modal adaptive logic AJ
r
(based on S5) as well as the discussive logic D
r
2
that is defined from it. D
r
2
is a (non-monotonic) alternative for Jaśkowski’s paraconsistent system D
2
. Like D
2
, D
r
2
validates all single-premise rules of Classical Logic. However, for formulas that behave consistently, D
r
2
moreover validates all multiple-premise rules of Classical Logic. Importantly, and unlike in the case of D
2
, this does not require the introduction of discussive connectives. It is argued that this has clear advantages with respect to one of the main application contexts of discussive logics, namely the interpretation of discussions.*Research for this paper was indirectly supported by the Flemish Minister responsible for Science and Technology (contract BIL1/8). The author is indebted to Leon Horsten, Jo?o Marcos, Jerzy Perzanowski, Liza Verhoeven, and especially to the referee and to Diderik Batens for comments and suggestions. 相似文献
99.
Ramon Jansana 《Studia Logica》2006,83(1-3):31-48
Willem Blok was one of the founders of the field Abstract Algebraic Logic. The paper describes his research in this field.
Dedicated to the memory of Willem Johannes Blok 相似文献
100.
We introduce necessary and sufficient conditions for a (single-conclusion) sequent calculus to admit (reductive) cut-elimination.
Our conditions are formulated both syntactically and semantically. 相似文献