A Modal-Layered Resolution Calculus for K

Nalon, Cláudia; Hustadt, Ullrich; Dixon, Clare

doi:10.1007/978-3-319-24312-2_13

Cited by 10 publications

(12 citation statements)

References 11 publications

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“…The calculi presented in [33,34] are both clausal. We present the normal form described in [34], as this normal form can be also used to simulate the one given in [33]. A formula to be tested for local or global satisfiability is first translated into a normal form called Separated Normal Form with Modal Levels, SNF ml .…”

Section: Layered Normal Formmentioning

confidence: 99%

“…Lemma 1 [34] Let ϕ ∈ WFF K be a formula and let t be a propositional symbol not occurring in ϕ. Then: (1) ϕ is locally satisfiable if, and only if, 0 : t ∧ ρ(0 : t ⇒ ϕ) is satisfiable; (2) ϕ is globally satisfiable if, and only if, * : t ∧ ρ( * : t ⇒ ϕ) is satisfiable.…”

Section: Layered Normal Formmentioning

confidence: 99%

“…We will focus on the resolution-based methods for K n which are presented in [33,34]. Both calculi are clausal: a formula to be tested for satisfiability is first translated into a normal form, to which a set of inference rules are applied.…”

Section: Introductionmentioning

confidence: 99%

“…For dealing with modal clauses, a set of hyper-resolution rules [44] are applied to modal and propositional clauses. The main difference between those proof methods resides in their normal form: in [33], for completeness, all clauses are considered for application of the resolution rules; whilst in [34], because clauses are labelled, the resolution rules only need to be applied when the labels of clauses can be unified. Differently from other calculi which use labels for guiding the application of inference rules [3,5,10,11,54,55], the labels in the clausal form given in [34] do not refer to worlds, but to the modal layer (i.e.…”

Section: Introductionmentioning

confidence: 99%

“…This paper extends the work in [35] providing full details of the prover, its main control loop, pre-processing options, notions of redundancy, refinements and strategies. The prover is based on the calculus presented in [34] and its sources are available at [36]. We also provide experimental results comparing K S P with other provers and analysing some of the combinations of refinements and strategies.…”

Section: Introductionmentioning

confidence: 99%

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A Resolution-Based Theorem Prover for $${\textsf {K}}_{n}^{}$$Kn: Architecture, Refinements, Strategies and Experiments

2018

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In this paper we describe the implementation of K S P, a resolution-based prover for the basic multimodal logic K n. The prover implements a resolution-based calculus for both local and global reasoning. The user can choose different normal forms, refinements of the basic resolution calculus, and strategies. We describe these options in detail and discuss their implications. We provide experiments comparing some of these options and comparing the prover with other provers for this logic.

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Section: Layered Normal Formmentioning

confidence: 99%

Section: Layered Normal Formmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Resolution-Based Theorem Prover for $${\textsf {K}}_{n}^{}$$Kn: Architecture, Refinements, Strategies and Experiments

2018

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Efficient Local Reductions to Basic Modal Logic

Papacchini

Nalon

Hustadt

et al. 2021

Automated Deduction – CADE 28

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We present novel reductions of the propositional modal logics "Image missing" , "Image missing" , "Image missing" , "Image missing" and "Image missing" to Separated Normal Form with Sets of Modal Levels. The reductions result in smaller formulae than the well-known reductions by Kracht and allow us to use the local reasoning of the prover "Image missing" to determine the satisfiability of modal formulae in these logics. We show experimentally that the combination of our reductions with the prover "Image missing" performs well when compared with a specialised resolution calculus for these logics and with the b̆uilt-in reductions of the first-order prover SPASS.

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Buy One Get 14 Free: Evaluating Local Reductions for Modal Logic

Nalon,

Hustadt,

Papacchini

et al. 2023

Lecture Notes in Computer Science

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We are interested in widening the reasoning support for propositional modal logics in the so-called modal cube. The modal cube consists of extensions of the basic modal logic $$\textsf{K}_{}$$ K with an arbitrary combination of the modal axioms $$\textsf{B}$$ B , $$\textsf{D}$$ D , $$\textsf{T}$$ T , $$\textsf{4}$$ 4 and $$\textsf{5}$$ 5 . We revisit recently developed local reductions from all logics in the modal cube to a normal form comprising sets of clausal formulae with associated modal levels. We extend these reductions further to the basic modal logic $$\textsf{K}_{}$$ K , called definitional reductions. This enables any prover for $$\textsf{K}_{}$$ K to be used to solve the satisfiability problem for all logics in the modal cube. We also present alternative, axiomatic, reductions based on ideas originally proposed by Kracht, providing new theoretical results and improved bounds on the size of the reductions. We compare both sets of reductions combined with state-of-the-art provers for $$\textsf{K}_{}$$ K on a large set of parametric benchmarks for all logics in the modal cube. The results show that the provers perform better with reductions based on the clausal normal form than the axiomatic reductions.

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A Modal-Layered Resolution Calculus for K

Cited by 10 publications

References 11 publications

A Resolution-Based Theorem Prover for $${\textsf {K}}_{n}^{}$$Kn: Architecture, Refinements, Strategies and Experiments

A Resolution-Based Theorem Prover for $${\textsf {K}}_{n}^{}$$Kn: Architecture, Refinements, Strategies and Experiments

Efficient Local Reductions to Basic Modal Logic

Buy One Get 14 Free: Evaluating Local Reductions for Modal Logic

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