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221.
222.
Probabilistic Entailment and a Non-Probabilistic Logic 总被引:1,自引:0,他引:1
223.
A plausible and popular rule governing the scope of truth-functional logic is shown to be indequate. The argument appeals to the existence of truth-functional paraphrases which are logically independent of their natural language counterparts. A more adequate rule is proposed. 相似文献
224.
B. H. Slater has argued that there cannot be any truly paraconsistent logics, because it's always more plausible to suppose whatever negation symbol is used in the language is not a real negation, than to accept the paraconsistent reading. In this paper I neither endorse nor dispute Slater's argument concerning negation; instead, my aim is to show that as an argument against paraconsistency, it misses (some of) the target. A important class of paraconsistent logics — the preservationist logics — are not subject to this objection. In addition I show that if we identify logics by means of consequence relations, at least one dialetheic logic can be reinterpreted in preservationist (non-dialetheic) terms. Thus the interest of paraconsistent consequence relations — even those that emerge from dialetheic approaches — does not depend on the tenability of dialetheism. Of course, if dialetheism is defensible, then paraconsistent logic will be required to cope with it. But the existence (and interest) of paraconsistent logics does not depend on a defense of dialetheism. 相似文献
225.
We introduce several restricted versions of the structural rules in the implicational fragment of Gentzen's sequent calculus
LJ. For example, we permit the applications of a structural rule only if its principal formula is an implication. We investigate
cut-eliminability and theorem-equivalence among various combinations of them. The results include new cut-elimination theorems
for the implicational fragments of the following logics: relevant logic E, strict implication S4, and their neighbors (e.g.,
E-W and S4-W); BCI-logic, BCK-logic, relevant logic R, and the intuitionistic logic.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
226.
227.
Marcus Kracht 《Journal of Philosophical Logic》1998,27(1):49-73
In this paper we will study the properties of the least extension n() of a given intermediate logic by a strong negation. It is shown that the mapping from to n() is a homomorphism of complete lattices, preserving and reflecting finite model property, frame-completeness, interpolation and decidability. A general characterization of those constructive logics is given which are of the form n (). This summarizes results that can be found already in [13,14] and [4]. Furthermore, we determine the structure of the lattice of extensions of n(LC). 相似文献
228.
The semantical structures called T×W frames were introduced in (Thomason, 1984) for the Ockhamist temporal-modal language, O, which consists of the usual propositional language augmented with the Priorean operators P and F and with a possibility operator . However, these structures are also suitable for interpreting an extended language, SO, containing a further possibility operator s which expresses synchronism among possibly incompatible histories and which can thus be thought of as a cross-history simultaneity operator. In the present paper we provide an infinite set of axioms in SO, which is shown to be strongly complete forT ×W-validity. Von Kutschera (1997) contains a finite axiomatization of T×W-validity which however makes use of the Gabbay Irreflexivity Rule (Gabbay, 1981). In order to avoid using this rule, the proof presented here develops a new technique to deal with reflexive maximal consistent sets in Henkin-style constructions. 相似文献
229.
Athanassios Tzouvaras 《Journal of Philosophical Logic》1998,27(1):85-108
We extend the ordinary logic of knowledge based on the operator K and the system of axioms S5 by adding a new operator U, standing for the agent utters , and certain axioms and a rule for U, forming thus a new system KU. The main advantage of KU is that we can express in it intentions of the speaker concerning the truth or falsehood of the claims he utters and analyze them logically. Specifically we can express in the new language various notions of lying, as well as of telling the truth. Consequently, as long as lying or telling the truth about a fact is an intentional mode of the speaker, we can resolve the Liar paradox, or at least some of its variants, turning it into an ordinary (false or true) sentence. Also, using Kripke structures analogous to those employed by S. Kraus and D. Lehmann in [3] for modelling the logic of knowledge and belief, we offer a sound and complete semantics for KU. 相似文献
230.
Reiner Hähnle 《Studia Logica》1998,61(1):101-121
We provide tools for a concise axiomatization of a broad class of quantifiers in many-valued logic, so-called distribution quantifiers. Although sound and complete axiomatizations for such quantifiers exist, their size renders them virtually useless for practical purposes. We show that for quantifiers based on finite distributive lattices compact axiomatizations can be obtained schematically. This is achieved by providing a link between skolemized signed formulas and filters/ideals in Boolean set lattices. Then lattice theoretic tools such as Birkhoff's representation theorem for finite distributive lattices are used to derive tableau-style axiomatizations of distribution quantifiers. 相似文献