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2011 | 9 | 6 | 1354-1379
Tytuł artykułu

Logics for stable and unstable mereological relations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we present logics about stable and unstable versions of several well-known relations from mereology: part-of, overlap and underlap. An intuitive semantics is given for the stable and unstable relations, describing them as dynamic counterparts of the base mereological relations. Stable relations are described as ones that always hold, while unstable relations hold sometimes. A set of first-order sentences is provided to serve as axioms for the stable and unstable relations, and representation theory is developed in similar fashion to Stone’s representation theory for distributive lattices. First-order predicate logic and modal logic are presented with semantics based on structures with stable and unstable mereological relations. Completeness theorems for these logics are proved, as well as decidability in the case of the modal logic, hereditary undecidability in the case of the first-order logic, and NP-completeness for the satisfiability problem of the quantifier-free fragment of the first-order logic.
Wydawca
Czasopismo
Rocznik
Tom
9
Numer
6
Strony
1354-1379
Opis fizyczny
Daty
wydano
2011-12-01
online
2011-09-23
Twórcy
Bibliografia
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Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-011-0094-z
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