Prior’s Three-Valued Modal Logic Q and its Possible Applications | Zendy

Seiki Akama | Zendy; Yasunori Nagata | Zendy

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Prior’s Three-Valued Modal Logic <I>Q</I> and its Possible Applications

Author(s) -

Seiki Akama,

Yasunori Nagata

Publication year - 2007

Publication title -

journal of advanced computational intelligence and intelligent informatics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.172

H-Index - 20

eISSN - 1343-0130

pISSN - 1883-8014

DOI - 10.20965/jaciii.2007.p0105

Subject(s) - modal logic , normal modal logic , multimodal logic , accessibility relation , modal , completeness (order theory) , s5 , computer science , kripke semantics , dynamic logic (digital electronics) , epistemic modal logic , possible world , semantics (computer science) , discrete mathematics , calculus (dental) , algorithm , algebra over a field , theoretical computer science , mathematics , description logic , programming language , pure mathematics , epistemology , philosophy , physics , transistor , voltage , mathematical analysis , chemistry , quantum mechanics , polymer chemistry , dentistry , medicine

Prior proposed a three-valued modal logic Q as a “correct” modal logic from his philosophical motivations. Unfortunately, Prior’s Q and many-valued modal logic have been neglected in the tradition of many-valued and modal logic. In this paper, we introduce a version of three-valued Kripke semantics for Q , which aims to establish Prior’s ideas based on possible worlds. We investigate formal properties of Q and prove the completeness theorem of Q . We also compare our approach with others and suggest possible applications.

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