TY - JOUR
T1 - Neighborhood-sheaf semantics for first-order modal logic
AU - Kishida, Kohei
N1 - Funding Information:
1 This work is part of the VIDI research programme with number 639.072.904, which is financed by the Netherlands Organisation for Scientific Research. The author also wishes to thank the anonymous referees for helpful comments and suggestions. 2 Email: kishidakohei@gmail.com
PY - 2011/11/3
Y1 - 2011/11/3
N2 - This paper extends neighborhood semantics for propositional modal logic to the first-order case, by unifying topological-sheaf semantics (in [2]) for first-order S4 and Kripke-sheaf semantics (see [11] and [8], just for instance) for quantified K. It will be shown how to take a sheaf-like structure over a neighborhood frame, and the resulting semantics properly generalizes the two preceding sheaf semantics; it has a weaker modal logic (in which the rule N fails) sound and complete, while accommodating classical, full first-order logic with equality and function symbols.
AB - This paper extends neighborhood semantics for propositional modal logic to the first-order case, by unifying topological-sheaf semantics (in [2]) for first-order S4 and Kripke-sheaf semantics (see [11] and [8], just for instance) for quantified K. It will be shown how to take a sheaf-like structure over a neighborhood frame, and the resulting semantics properly generalizes the two preceding sheaf semantics; it has a weaker modal logic (in which the rule N fails) sound and complete, while accommodating classical, full first-order logic with equality and function symbols.
KW - First-order modal logic
KW - neighborhood semantics
KW - sheaf semantics
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U2 - 10.1016/j.entcs.2011.10.011
DO - 10.1016/j.entcs.2011.10.011
M3 - Article
AN - SCOPUS:80155194329
SN - 1571-0661
VL - 278
SP - 129
EP - 143
JO - Electronic Notes in Theoretical Computer Science
JF - Electronic Notes in Theoretical Computer Science
IS - 1
ER -