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Carlos A. Oller 《Journal of Applied Logic》2004,2(4):451-455
This paper introduces a technique for measuring the degree of (in)coherence of inconsistent sets of propositional formulas. The coherence of these sets of formulas is calculated using the minimal models of those sets in G. Priest's Logic of Paradox. The compatibility of the information expressed by a set of formulas with the background or domain knowledge can also be measured with this technique. In this way, Hunter's objections to many-valued paraconsistent logics as instruments for measuring (in)coherence are addressed. 相似文献
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Norihiro Kamide 《Studia Logica》2009,91(2):217-238
New propositional and first-order paraconsistent logics (called L
ω
and FL
ω
, respectively) are introduced as Gentzen-type sequent calculi with classical and paraconsistent negations. The embedding
theorems of L
ω
and FL
ω
into propositional (first-order, respectively) classical logic are shown, and the completeness theorems with respect to simple
semantics for L
ω
and FL
ω
are proved. The cut-elimination theorems for L
ω
and FL
ω
are shown using both syntactical ways via the embedding theorems and semantical ways via the completeness theorems.
Presented by Yaroslav Shramko and Heinrich Wansing 相似文献
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Logics for generally were introduced for handling assertions with vague notions,such as generally, most, several, etc., by generalized quantifiers, ultrafilter logic being an interesting case. Here, we show that ultrafilter logic can be faithfully embedded into a first-order theory of certain functions, called coherent. We also use generic functions (akin to Skolem functions) to enable elimination of the generalized quantifier. These devices permit using methods for classical first-order logic to reason about consequence in ultrafilter logic.Presented by André Fuhrmann 相似文献
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This paper is a contribution to the program of constructing formal representations
of pragmatic aspects of human reasoning. We propose a formalization within the framework of Adaptive Logics of the exclusivity
implicature governing the connective ‘or’.Keywords: exclusivity implicature, Adaptive Logics. 相似文献
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In this paper we study proof procedures for some variants of first-order modal logics, where domains may be either cumulative or freely varying and terms may be either rigid or non-rigid, local or non-local. We define both ground and free variable tableau methods, parametric with respect to the variants of the considered logics. The treatment of each variant is equally simple and is based on the annotation of functional symbols by natural numbers, conveying some semantical information on the worlds where they are meant to be interpreted.This paper is an extended version of a previous work where full proofs were not included. Proofs are in some points rather tricky and may help in understanding the reasons for some details in basic definitions. 相似文献
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In order to develop an account of scientific rationality, two problems need to be addressed: (i) how to make sense of episodes
of theory change in science where the lack of a cumulative development is found, and (ii) how to accommodate cases of scientific
change where lack of consistency is involved. In this paper, we sketch a model of scientific rationality that accommodates
both problems. We first provide a framework within which it is possible to make sense of scientific revolutions, but which
still preserves some (partial) relations between old and new theories. The existence of these relations help to explain why
the break between different theories is never too radical as to make it impossible for one to interpret the process in perfectly
rational terms. We then defend the view that if scientific theories are taken to be quasi-true, and if the underlying logic
is paraconsistent, it’s perfectly rational for scientists and mathematicians to entertain inconsistent theories without triviality.
As a result, as opposed to what is demanded by traditional approaches to rationality, it’s not irrational to entertain inconsistent
theories. Finally, we conclude the paper by arguing that the view advanced here provides a new way of thinking about the foundations
of science. In particular, it extends in important respects both coherentist and foundationalist approaches to knowledge,
without the troubles that plague traditional views of scientific rationality. 相似文献
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Extensions of Natural Deduction to Substructural Logics of IntuitionisticLogic are shown: Fragments of Intuitionistic Linear, Relevantand BCK Logic. Rules for implication, conjunction, disjunctionand falsum are defined, where conjunction and disjunction respectcontexts of assumptions. So, conjunction and disjunction areadditive in the terminology of linear logic. Explicit contractionand weakening rules are given. It is shown that conversionsand permutations can be adapted to all these rules, and thatweak normalisation and subformula property holds. The resultsgeneralise to quantification. 相似文献