Meeting strength in substructural logics | Zendy

Yde Venema | Zendy

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Meeting strength in substructural logics

Author(s) -

Yde Venema

Publication year - 1995

Publication title -

studia logica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.736

H-Index - 39

eISSN - 1572-8730

pISSN - 0039-3215

DOI - 10.1007/bf01058530

Subject(s) - soundness , completeness (order theory) , operator (biology) , mathematics , proof theory , semantics (computer science) , kripke semantics , algebra over a field , calculus (dental) , t norm fuzzy logics , computer science , monoidal t norm logic , equivalence (formal languages) , discrete mathematics , mathematical proof , pure mathematics , theoretical computer science , programming language , artificial intelligence , intermediate logic , description logic , chemistry , gene , fuzzy logic , mathematical analysis , membership function , biochemistry , geometry , fuzzy set , transcription factor , medicine , dentistry , repressor , fuzzy number

This paper contributes to the theory of hybrid substructural logics, i.e. weak logics given by a Gentzen-style proof theory in which there is only a limited possibility to use structural rules. Following the literature, we use an operator to mark formulas to which the extra structural rules may be applied. New in our approach is that we do not see thisr as a modality, but rather as the meet of the marked formula with a special type Q. In this way we can make the specic structural behaviour of marked formulas more explicit. The main motivation for our approach is that we can provide a nice, intuitive semantics for hybrid substructural logics. Soundness and completeness for this semantics are proved; besides this we consider some proof-theoretical aspects like cut-elimination and embeddings of the 'strong' system in the hybrid one.

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