Using the Universal Modality: Gains and Questions

Goranko, Valentin; Passy, Solomon

doi:10.1093/logcom/2.1.5

Cited by 205 publications

(172 citation statements)

References 21 publications

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“…is valid (this can related to Corollary 5.3 in [GP92]). So the problem of determining whether S |= A holds where S is finite set of formulae and A ∈ for(φ 0 ) is co-NP-complete (remember the validity problem for E is co-NP-complete).…”

Section: Logical Consequencementioning

confidence: 56%

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A simple tableau system for the logic of elsewhere

Demri¹

1996

Theorem Proving With Analytic Tableaux and Related Methods

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Abstract. We analyze different features related to the mechanization of von Wright's logic of elsewhere E. First, we give a new proof of the NP-completeness of the satisfiability problem (giving a new bound for the size of models of the satisfiable formulae) and we show that this problem becomes linear-time when the number of propositional variables is bounded. Although E and the well-known propositional modal S5 share numerous common features we show that E is strictly more expressive than S5 (in a sense to be specified). Second, we present a prefixed tableau system for E and we prove both its soundness and completeness. Two extensions of this system are also defined, one related to the logical consequence relation and the other related to the addition of modal operators (without increasing the expressive power). An example of tableau proof is also presented. Different continuations of this work are proposed, one of them being to implement the defined tableau system, another one being to extend this system to richer logics that can be found in the literature.

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Section: Logical Consequencementioning

confidence: 56%

“…operator and different other modal operators such as the different logics studied for example in [GPT87,GG93,GP92,Rij92]. For instance, it is possible to admit in the same language the classical modal operator 2 and the difference operator [ =].…”

Section: An Extended Calculusmentioning

confidence: 99%

A simple tableau system for the logic of elsewhere

Demri¹

1996

Theorem Proving With Analytic Tableaux and Related Methods

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“…We shall also consider modal logics endowed with a universal modality [36], which corresponds to the universal relation in Kripke semantics (see below). The language of these logics contains an additional unary connective ∀ (the formula ∃A is defined as ¬∀¬A).…”

Section: Syntaxmentioning

confidence: 99%

Unification in modal and description logics

Baader

Ghilardi

2010

Logic Journal of IGPL

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“…• Second, the useful universal box 2 u ϕ, which is well-known from modal logic [GP92], has the following semantics:…”

Section: Structuresmentioning

confidence: 99%

Modal Logics of Topological Relations

Lutz¹,

Wolter²

2006

Logical Methods in Computer Science

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Abstract. Logical formalisms for reasoning about relations between spatial regions play a fundamental role in geographical information systems, spatial and constraint databases, and spatial reasoning in AI. In analogy with Halpern and Shoham's modal logic of time intervals based on the Allen relations, we introduce a family of modal logics equipped with eight modal operators that are interpreted by the Egenhofer-Franzosa (or RCC8) relations between regions in topological spaces such as the real plane. We investigate the expressive power and computational complexity of logics obtained in this way. It turns out that our modal logics have the same expressive power as the two-variable fragment of first-order logic, but are exponentially less succinct. The complexity ranges from (undecidable and) recursively enumerable to Π 1 1 -hard, where the recursively enumerable logics are obtained by considering substructures of structures induced by topological spaces. As our undecidability results also capture logics based on the real line, they improve upon undecidability results for interval temporal logics by Halpern and Shoham. We also analyze modal logics based on the five RCC5 relations, with similar results regarding the expressive power, but weaker results regarding the complexity.

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Using the Universal Modality: Gains and Questions

Abstract: The paper investigates a simple and natural enrichment of the usual modal language !£ = !£ Show more

Cited by 205 publications

References 21 publications

A simple tableau system for the logic of elsewhere

A simple tableau system for the logic of elsewhere

Unification in modal and description logics

Modal Logics of Topological Relations

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