A bi-intuitionistic modal logic: Foundations and automation

Stell, John G.; Schmidt, Renate A.; Rydeheard, David E.

doi:10.1016/j.jlamp.2015.11.003

Cited by 17 publications

(30 citation statements)

References 11 publications

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“…When it can no longer be delayed, we tend to apply rules creating fewer branches earlier than those creating more branches, unless looking ahead allows us to see that several branches created by an inference step can be closed quickly. In a prover, where everything is automated, the overhead of branching is high as well, so that similar strategies are useful and have been shown to give significant speed-ups, as we found for example in the evaluations undertaken in [14,23]. Similar considerations and better performance have motivated the development and use of hypertableau, hyperresolution or selection-based resolution methods [3,4,7,16].…”

Section: Introductionmentioning

confidence: 85%

“…In [23] we applied the tableau synthesis framework and atomic rule refinement in the creation of terminating tableau calculi for a biintuitionistic logic with interacting modal operators, called BISKT. This logic can be equivalently embedded into a tense logic Kt(H, R) with several interacting modalities [18] via an extension of the standard embedding of intuitionistic propositional logic into modal logic S4.…”

Section: Km Extended With the Rulesmentioning

confidence: 99%

“…Kt(H, R) was subject to an investigation of the numerous possibilities of defining tableau calculi for modal logics, and their relative efficiency [18]. Interestingly, we found that the tableau calculi of BISKT [23] exhibited better performance than those of Kt(H, R) [18], which we attribute to the greater constraining power of atomic rule refinement in the style of calculus used for BISKT.…”

Section: Km Extended With the Rulesmentioning

confidence: 99%

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Rule Refinement for Semantic Tableau Calculi

Tishkovsky

Schmidt

2017

Lecture Notes in Computer Science

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Abstract. This paper investigates refinement techniques for semantic tableau calculi. The focus is on techniques to reduce branching in inference rules and thus allow more effective ways of carrying out deductions. We introduce an easy to apply, general principle of atomic rule refinement, which depends on a purely syntactic condition that can be easily verified. The refinement has a wide scope, for example, it is immediately applicable to inference rules associated with frame conditions of modal logics, or declarations of role properties in description logics, and it allows for routine development of hypertableau-like calculi for logics with disjunction and negation. The techniques are illustrated on Humberstone's modal logic Km(¬) with modal operators defined with respect to both accessibility and inaccessibility, for which two refined calculi are given.

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Section: Introductionmentioning

confidence: 85%

Section: Km Extended With the Rulesmentioning

confidence: 99%

Section: Km Extended With the Rulesmentioning

confidence: 99%

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Rule Refinement for Semantic Tableau Calculi

Tishkovsky

Schmidt

2017

Lecture Notes in Computer Science

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“…This paper has used a correspondence between partially ordered partitions and certain reflexive transitive relations to find a simple way of defining approximation operators on ordered information systems. Further work is continuing on connections between these approximation operators and the bi-intuitionistic modal logic using relations on hypergraphs that was introduced in [17]. This is likely to provide a way of generalizing information logics [4] to the partially ordered setting.…”

Section: Approximation Operatorsmentioning

confidence: 99%

Ordered Information Systems and Graph Granulation

Stell

2016

Rough Sets

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Abstract. The concept of an Information System, as used in Rough Set theory, is extended to the case of a partially ordered universe equipped with a set of order preserving attributes. These information systems give rise to partitions of the universe where the set of equivalence classes is partially ordered. Such ordered partitions correspond to relations on the universe which are reflexive and transitive. This correspondence allows the definition of approximation operators for an ordered information system by using the concepts of opening and closing from mathematical morphology. A special case of partial orders are graphs and hypergraphs and these provide motivation for the need to consider approximations on partial orders.

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“…I was delighted to learn that Onishi in his work comes to the same conclusion and presents a display treatment of impossibility and unnecessity over bi-intuitionistic logic. Modal bi-intuitionistic logic was also considered, for instance, in [30].…”

Section: Introductionmentioning

confidence: 99%

On Displaying Negative Modalities

Drobyshevich

2017

LLP

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Abstract. We extend Takuro Onishi's result on displaying substructural negations by formulating display calculi for non-normal versions of impossibility and unnecessity operators, called regular and co-regular negations, respectively, by Dimiter Vakarelov. We make a number of connections between Onishi's work and Vakarelov's study of negation. We also prove a decidability result for our display calculus, which can be naturally extended to obtain decidability results for a large number of display calculi for logics with negative modal operators.

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A bi-intuitionistic modal logic: Foundations and automation

Cited by 17 publications

References 11 publications

Rule Refinement for Semantic Tableau Calculi

Rule Refinement for Semantic Tableau Calculi

Ordered Information Systems and Graph Granulation

On Displaying Negative Modalities

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