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- W4289103995 abstract "Abstract The characterizing properties of a proof-theoretical presentation of a given logic may hang on the choice of proof formalism, on the shape of the logical rules and of the sequents manipulated by a given proof system, on the underlying notion of consequence, and even on the expressiveness of its linguistic resources and on the logical framework into which it is embedded. Standard (one-dimensional) logics determined by (non-deterministic) logical matrices are known to be axiomatizable by analytic and possibly finite proof systems as soon as they turn out to satisfy a certain constraint of sufficient expressiveness. In this paper we introduce a recipe for cooking up a two-dimensional logical matrix (or -matrix) by the combination of two (possibly partial) non-deterministic logical matrices. We will show that such a combination may result in -matrices satisfying the property of sufficient expressiveness, even when the input matrices are not sufficiently expressive in isolation, and we will use this result to show that one-dimensional logics that are not finitely axiomatizable may inhabit finitely axiomatizable two-dimensional logics, becoming, thus, finitely axiomatizable by the addition of an extra dimension. We will illustrate the said construction using a well-known logic of formal inconsistency called mCi . We will first prove that this logic is not finitely axiomatizable by a one-dimensional (generalized) Hilbert-style system. Then, taking advantage of a known 5-valued non-deterministic logical matrix for this logic, we will combine it with another one, conveniently chosen so as to give rise to a -matrix that is axiomatized by a two-dimensional Hilbert-style system that is both finite and analytic." @default.
- W4289103995 created "2022-08-01" @default.
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- W4289103995 date "2022-01-01" @default.
- W4289103995 modified "2023-09-30" @default.
- W4289103995 title "Finite Two-Dimensional Proof Systems for Non-finitely Axiomatizable Logics" @default.
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- W4289103995 doi "https://doi.org/10.1007/978-3-031-10769-6_37" @default.
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