Modal interpolation via nested sequents

Fitting, Melvin; Kuznets, Roman

doi:10.1016/j.apal.2014.11.002

Cited by 22 publications

(19 citation statements)

References 8 publications

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“…The literature on nested sequents is also rich: they have been used to establish algorithmic properties on a wide range of logics (e.g. [2,10,11,13,26]). The explicit use of ordinal approximations in the language of µ-calculus is a feature that has been used by other authors studying fixed-point logics.…”

Section: Related Workmentioning

confidence: 99%

An Infinitary Treatment of Full Mu-Calculus

Afshari

Jäger

Leigh

2019

Logic, Language, Information, and Computation

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We explore the proof theory of the modal µ-calculus with converse, aka the 'full µ-calculus'. Building on nested sequent calculi for tense logics and infinitary proof theory of fixed point logics, a cut-free sound and complete proof system for full µ-calculus is proposed. As a corollary of our framework, we also obtain a direct proof of the regular model property for the logic: every satisfiable formula has a tree model with finitely many distinct subtrees. To obtain the results we appeal to the basic theory of well-quasi-orderings in the spirit of Kozen's proof of the finite model property for µ-calculus without converse.

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Section: Related Workmentioning

confidence: 99%

An Infinitary Treatment of Full Mu-Calculus

Afshari

Jäger

Leigh

2019

Logic, Language, Information, and Computation

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“…For a class of Kripke models C L satisfying (15), an interpolant transformation for the rule (14) is shown in Table 10. 6 Proof. It is easy to see that the common propositional atoms condition is preserved.…”

Section: Telescopic Rulesmentioning

confidence: 99%

“…In Sect. 6, we extend the method to Horn-like geometric rules. and apply our findings to the infinite family of Geach logics.…”

Section: Introductionmentioning

confidence: 99%

Proving Craig and Lyndon Interpolation Using Labelled Sequent Calculi

Kuznets¹

2016

Logics in Artificial Intelligence

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We have recently presented a general method of proving the fundamental logical properties of Craig and Lyndon Interpolation (IPs) by induction on derivations in a wide class of internal sequent calculi, including sequents, hypersequents, and nested sequents. Here we adapt the method to a more general external formalism of labelled sequents and provide sufficient criteria on the Kripke-frame characterization of a logic that guarantee the IPs. In particular, we show that classes of frames definable by quantifier-free Horn formulas correspond to logics with the IPs. These criteria capture the modal cube and the infinite family of transitive Geach logics.

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“…Accomplishing such a task would prove beneficial, since systems built within the nested formalism tend to be more economical (viz. they utilize simpler data structures) than those built within the labelled formalism, and have proven well-suited for the construction of analytic calculi [2,3,19], for writing decision algorithms [14,33], and for verifying interpolation [12,24].…”

Section: Introductionmentioning

confidence: 99%

Nested Sequents for Intuitionistic Modal Logics via Structural Refinement

Lyon

2021

Lecture Notes in Computer Science

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We employ a recently developed methodology-called structural refinement-to extract nested sequent systems for a sizable class of intuitionistic modal logics from their respective labelled sequent systems. This method can be seen as a means by which labelled sequent systems can be transformed into nested sequent systems through the introduction of propagation rules and the elimination of structural rules, followed by a notational translation. The nested systems we obtain incorporate propagation rules that are parameterized with formal grammars, and which encode certain frame conditions expressible as first-order Horn formulae that correspond to a subclass of the Scott-Lemmon axioms. We show that our nested systems are sound, cut-free complete, and admit hp-admissibility of typical structural rules.

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Modal interpolation via nested sequents

Cited by 22 publications

References 8 publications

An Infinitary Treatment of Full Mu-Calculus

An Infinitary Treatment of Full Mu-Calculus

Proving Craig and Lyndon Interpolation Using Labelled Sequent Calculi

Nested Sequents for Intuitionistic Modal Logics via Structural Refinement

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