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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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  • [18] Vakarelov D., Logical analysis of positive and negative similarity relations in property systems, In: 1st World Conference on the Fundamentals of Artificial Intelligence, Paris, July 1–5, 1991, 491–499
  • [19] Vakarelov D., A modal logic for set relations, In: 10th International Congress of Logic, Methodology and Philosophy of Science, Florence, August 19–25, 1995, 183
  • [20] Vakarelov D., A modal approach to dynamic ontology: modal mereotopology, Logic Log. Philos., 2008, 17(1–2), 163–183
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Typ dokumentu

Bibliografia

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bwmeta1.element.doi-10_2478_s11533-011-0094-z
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