The Resolution Principle

Leitsch, Alexander; Fermüller, Christian G.

doi:10.1007/1-4020-3092-4_2

Cited by 1 publication

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References 44 publications

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“…Thus, since the signed many-valued logic is, one may say, rather close to propositional logic and is employed in a wide range of reasoning scenarios and applications e.g., [21,79,73,8,47] (discussed in related work), we have selected its sub-class, called regular logic, in order to determine a first tractable non-clausal class within approximate reasoning.…”

Section: Introductionmentioning

confidence: 99%

A First Polynomial Non-Clausal Class in Many-Valued Logic

Imaz¹

2021

Preprint

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The relevance of polynomial formula classes to deductive efficiency motivated their search, and currently, a great number of such classes is known. Nonetheless, they have been exclusively sought in the setting of clausal form and propositional logic, which is of course expressively limiting for real applications. As a consequence, a first polynomial propositional class in non-clausal (NC) form has recently been proposed.Along these lines and towards making NC tractability applicable beyond propositional logic, firstly, we define the Regular many-valued Horn Non-Clausal class, or RH, obtained by suitably amalgamating both regular classes: Horn and NC.Secondly, we demonstrate that the relationship between (1) RH and the regular Horn class is that syntactically RH subsumes the Horn class but that both classes are equivalent semantically; and between (2) RH and the regular non-clausal class is that RH contains all NC formulas whose clausal form is Horn.Thirdly, we define Regular Non-Clausal Unit-Resolution, or RUR NC , and prove both that it is complete for RH and that checks its satisfiability in polynomial time. The latter fact shows that our intended goal is reached since RH is many-valued, non-clausal and tractable.As RH and RUR NC are, both, basic in the DPLL scheme, the most efficient in propositional logic, and can be extended to some other non-classical logics, we argue that they pave the way for efficient non-clausal DPLL-based approximate reasoning.Field: Tractable Approximate Automated Reasoning.

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Section: Introductionmentioning

confidence: 99%

A First Polynomial Non-Clausal Class in Many-Valued Logic

Imaz¹

2021

Preprint

View full text Add to dashboard Cite

show abstract

The Resolution Principle

Cited by 1 publication

References 44 publications

A First Polynomial Non-Clausal Class in Many-Valued Logic

A First Polynomial Non-Clausal Class in Many-Valued Logic

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