Classically complete modal relevant logics | Zendy

Mares Edwin D. | Zendy

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Classically complete modal relevant logics

Author(s) -

Mares Edwin D.

Publication year - 1993

Publication title -

mathematical logic quarterly

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.473

H-Index - 28

eISSN - 1521-3870

pISSN - 0942-5616

DOI - 10.1002/malq.19930390119

Subject(s) - ackermann function , modal logic , mathematics , normal modal logic , t norm fuzzy logics , corollary , s5 , accessibility relation , completeness (order theory) , modal , dynamic logic (digital electronics) , extension (predicate logic) , multimodal logic , variety (cybernetics) , modal μ calculus , intermediate logic , kripke semantics , classical logic , calculus (dental) , discrete mathematics , computer science , theoretical computer science , description logic , artificial intelligence , programming language , mathematical analysis , fuzzy logic , inverse , dentistry , transistor , voltage , chemistry , membership function , geometry , quantum mechanics , fuzzy set , statistics , physics , medicine , polymer chemistry

A variety of modal logics based on the relevant logic R are presented. Models are given for each of these logics and completeness is shown. It is also shown that each of these logics admits Ackermann's rule γ and as a corollary of this it is proved that each logic is a conservative extension of its counterpart based on classical logic, hence we call them “classically complete”. MSC: 03B45, 03B46.

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