Inconsistency-Tolerant Bunched Implications
نویسندگان
چکیده
منابع مشابه
Classical Logic of Bunched Implications
We consider a classical (propositional) version, CBI, of O’Hearn and Pym’s logic of bunched implications (BI) from a modeland prooftheoretic perspective. We present a class of classical models of BI which extend the usual BI-models, based on partial commutative monoids, with an algebraic notion of “resource negation”. This class of models gives rise to natural definitions of multiplicative fals...
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Many logics for AI applications that are defined by denotational semantics are trivialized in the presence of inconsistency. It is therefore often desirable, and practically useful, to refine such logics in a way that inconsistency does not cause the derivation of any formula, and, at the same time, inferences with respect to consistent premises are not affected. In this paper, we introduce a g...
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We introduce a logic BI in which a multiplicative (or linear) and an additive (or intuitionistic) implication live side-by-side. The propositional version of BI arises from an analysis of the proof-theoretic relationship between conjunction and implication; it can be viewed as a merging of intuitionistic logic and multiplicative intuitionistic linear logic. The naturality of BI can be seen cate...
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A game semantics of the (−−∗,→)-fragment of the logic of bunched implications, BI, is presented. To date, categorical models of BI have been restricted to two kinds: functor category models; and the category Cat itself. The game model is not of this kind. Rather, it is based on Hyland-Ong-Nickau-style games and embodies a careful analysis of the notions of resource sharing and separation inhere...
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Engberg and Winskel's Petri net semantics of linear logic is reconsidered , from the point of view of the logic BI of bunched implications. We rst show how BI can be used to overcome a number of diiculties pointed out by Engberg and Winskel, and we argue that it provides a more natural logic for the net semantics. We then brieey consider a more expressive logic based on an extension of BI with ...
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ژورنال
عنوان ژورنال: International Journal of Approximate Reasoning
سال: 2013
ISSN: 0888-613X
DOI: 10.1016/j.ijar.2012.11.004