A Proof System for Contact Relation Algebras

Abstract. Each information system (or data table) leads to a hierarchy of binary relations on the object set in a natural way; these relational systems can serve as frames for the semantics of modal logics. While relations of indiscernibility and their logics have been frequently studied, the situation in the case of relations which distinguish objects is much less clear. In this paper, we present complete logical systems for relations of complementarity derived from information systems.Mathematics Subject Classification: 03B45, 03B60.

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“…A complete relational proof system for relation algebras generated by a contact relation [13] was given in [12].…”

Section: Discussionmentioning

confidence: 99%

Logics of Complementarity in Information Systems

Düntsch

Orłowska

2000

MLQ - Math. Log. Quart.

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“…An example in [27] shows that there is a CRA with infinitely many atoms below 1 , and thus, by a result of Andréka et al [3], the equational logic of CRAs is undecidable. …”

Section: If a Formula Is Valid Then It Has A Closed Proof Treementioning

confidence: 99%

Axioms, Algebras and Topology

Bennett

Düntsch²

2007

Handbook of Spatial Logics

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“…Proof systems in the style of RasiowaSikorski can be also formulated for many other logics. They were studied in [5], [7], [12], [9], among others. A survey of signed dual tableaux systems can be found in [6].…”

Section: Rasiowa-sikorski System For Fmentioning

confidence: 99%

Tableaux and Dual Tableaux: Transformation of Proofs

Golińska-Pilarek

Orłowska

2007

Stud Logica

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We present two proof systems for first-order logic with identity and without function symbols. The first one is an extension of the Rasiowa-Sikorski system with the rules for identity. This system is a validity checker. The rules of this system preserve and reflect validity of disjunctions of their premises and conclusions. The other is a Tableau system, which is an unsatisfiability checker. Its rules preserve and reflect unsatisfiability of conjunctions of their premises and conclusions. We show that the two systems are dual to each other. The duality is expressed in a formal way which enables us to define a transformation of proofs in one of the systems into the proofs of the other.

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A Proof System for Contact Relation Algebras

Cited by 20 publications

References 19 publications

Logics of Complementarity in Information Systems

Logics of Complementarity in Information Systems

Axioms, Algebras and Topology

Tableaux and Dual Tableaux: Transformation of Proofs

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