Modal Tableaux with Propagation Rules and Structural Rules

Castilho, Marcos; Cerro, Luís Fariñas del; Gasquet, Olivier; Herzig, Andreas

doi:10.3233/fi-1997-323404

Cited by 29 publications

(27 citation statements)

References 6 publications

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“…• and in which every applicable rule has been applied. The following result has been stated and proved in [5]:…”

Section: Properties Rulesmentioning

confidence: 95%

“…In this section, we consider two subsections, one corresponding to the wellknown monomodal cases KD4, KD4.C and KD4.D (Since the results of this subsection appeared in previous publications ( [5], [6]), the corresponding proofs are not given), the other corresponding to a multimodal logic with two modal operators and an interaction axiom that allows the permutation of the modal operators.…”

Section: The Monomodal Casementioning

confidence: 99%

“…The above algorithm must be applied until for some i, either Y i is closed or Y i+1 = Y i (i.e. there are marked nodes on each branch) 5 .…”

Section: Kernels For Kd4mentioning

confidence: 99%

“…In [5], a general completeness proof based in tableaux has been presented for a large family of modal logics. In the line of this previous work, we presented in [6] strategies for some of these logics, and obtain thus decision procedures for logics based on transitivity plus density or confluence as characteristic axioms.…”

Section: Introductionmentioning

confidence: 99%

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Minimal structures for modal tableaux: Some examples

Cerro

Gasquet

2004

LLP

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In this paper we present some examples of decision procedures based on tableau calculus for some mono-and multimodal logics having a semantics involving properties that are not easily representable in tree-like structures (like e.g. density, confluence and persistence). We show how to handle them in our framework by generalizing usual tableaux (which are trees) to richer structures: rooted directed acyclic graphs.

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“…• and in which every applicable rule has been applied. The following result has been stated and proved in [5]:…”

Section: Properties Rulesmentioning

confidence: 95%

Section: The Monomodal Casementioning

confidence: 99%

“…The above algorithm must be applied until for some i, either Y i is closed or Y i+1 = Y i (i.e. there are marked nodes on each branch) 5 .…”

Section: Kernels For Kd4mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Minimal structures for modal tableaux: Some examples

Cerro

Gasquet

2004

LLP

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“…Therefore, we restrict attention here to methods related to logics of confluence. Tableaux methods for logics of confluence where the mono-modal axioms T, D, B, 4, 5, De (for density, the converse of 4), and G are valid, can be found in [7,9]. For each of those axioms, a tableau inference rule is given.…”

Section: Closing Remarksmentioning

confidence: 99%

Clausal Resolution for Modal Logics of Confluence

Nalon

Marcos²,

Dixon

2014

Automated Reasoning

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Abstract. We present a clausal resolution-based method for normal multimodal logics of confluence, whose Kripke semantics are based on frames characterised by appropriate instances of the Church-Rosser property. Here we restrict attention to eight families of such logics. We show how the inference rules related to the normal logics of confluence can be systematically obtained from the parametrised axioms that characterise such systems. We discuss soundness, completeness, and termination of the method. In particular, completeness can be modularly proved by showing that the conclusions of each newly added inference rule ensures that the corresponding conditions on frames hold. Some examples are given in order to illustrate the use of the method.

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