David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Journal of Logic, Language and Information 5 (1):65-105 (1996)
This paper presents an information-based logic that is applied to the analysis of entailment, implicature and presupposition in natural language. The logic is very fine-grained and is able to make distinctions that are outside the scope of classical logic. It is independently motivated by certain properties of natural human reasoning, namely partiality, paraconsistency, relevance, and defeasibility: once these are accounted for, the data on implicature and presupposition comes quite naturally.The logic is based on the family of semantic spaces known as bilattices, originally proposed by Ginsberg (1988), and used extensively by Fitting (1989, 1992). Specifically, the logic is based on a subset of bilattices that I call evidential bilattices, constructed as the Cartesian product of certain algebras with themselves. The specific details of the epistemic agent approach of the logical system is derived from the work of Belnap (1975, 1977), augmented by the use of evidential links for inferencing. An important property of the system is that it has been implemented using an extension of Fitting's work on bilattice logic programming (1989, 1991) to build a model-based inference engine for the augmented Belnap logic. This theorem prover is very efficient for a reasonably wide range of inferences.
|Keywords||Evidential reasoning natural language semantics presupposition defeasible reasoning relevance logic bilattice logic|
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Norihiro Kamide & Heinrich Wansing (2011). Completeness and Cut-Elimination Theorems for Trilattice Logics. Annals of Pure and Applied Logic 162 (10):816-835.
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Melvin Fitting (2006). Bilattices Are Nice Things. In T. Bolander, V. Hendricks & S. A. Pedersen (eds.), Self-Reference. Csli Publications.
Ofer Arieli & Arnon Avron (1996). Reasoning with Logical Bilattices. Journal of Logic, Language and Information 5 (1):25--63.
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