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Characterizing finite-valuedness
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DOI：10.1016/j.fss.2017.10.014.png)
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Abstract
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We introduce properties of consequence relations that provide abstract counterparts of different notions of finite-valuedness in logic. In particular, we obtain characterizations of logics that are determined (i) by a single finite matrix, (ii) by a finite set of finite matrices, and (iii) by a set of n-generated matrices for some natural number n. A crucial role is played in our proofs by two closely related notions, local tabularity and local finiteness. (C) 2017 Elsevier B.V. All rights reserved.
Keywords:
Logical matrix semantics
Many-valuedness
Finite-valuedness
Strong finiteness
Local tabularity
Local finiteness
Cancellation
Finite-determinedness
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