Non-clausal reasoning with propositional definite theories

Stachniak, Zbigniew

doi:10.1007/bfb0055921

Cited by 6 publications

(6 citation statements)

References 7 publications

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“…Generalized resolution 10,11 is one of non-clausal resolution methods to describe and deal with the complex problems more naturally, which attempts to reason by using formulae directly without translating them to clausal forms. Similar ideas for non-clausal resolution have also been proposed by Murray 13 , and further developed in 1,2,8,14,17,20,21,22 , as well as some refined resolution methods for improving the efficiency of non-clausal resolution investigated and reported in 23,25 . Meanwhile, the completeness of these methods has been Uncertainty is often associated with human's intelligent activities, it is rather difficult to represent and reason it only by numbers or symbols in classical logic.…”

Section: Introductionmentioning

confidence: 80%

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α-Generalized lock resolution method in linguistic truth-valued lattice-valued logic

Liu

et al. 2012

IJCIS

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This paper focuses on efficient non-clausal resolution-based automated reasoning methods and algorithms for a lattice-ordered linguistic truth-valued logic, which corresponds to extensions of α-lock resolution. Firstly, α-generalized lock resolution is proposed for lattice-valued propositional logic and first order logic, respectively, along with their concepts, soundness and completeness. Then, α-generalized lock resolution for first order linguistic truth-valued lattice-valued logic L V(n×2) F(X) is equivalently transformed into that for propositional logic L n P(X), which can greatly reduce the complexity of the resolution procedure. Finally, α-generalized linear semi-lock resolution is discussed, and its general algorithm is also contrived. This work provides more efficient and natural resolution automated reasoning scheme in linguistic truth-valued logic based on lattice implication algebra with the aim at establishing formal tools for symbolic natural language processing.

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Section: Introductionmentioning

confidence: 80%

“…2 a factor of Φ 2 for g-literals g 21 , g 22 , · · · , g 2r 2 , · · · , and Φ σ n n a factor of Φ n for gliterals g n1 , g n2 , · · · , g nr n , α ∈ L. If there exists g i1 with the minimal index in Φ…”

Section: α-Generalized Lock Resolution In Lf(x)mentioning

confidence: 99%

α-Generalized lock resolution method in linguistic truth-valued lattice-valued logic

Liu

et al. 2012

IJCIS

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“…Moreover, a number of approaches for NC satisfiability have been proposed and among them we mention: NC Resolution [151], NC DPLL solvers e.g. [158,91,186,115], path dissolution and anti-links [22,165], connection calculi [159], regular, connected tableaux [102], NC tableaux-like with reductions [95], SLD-resolution [180] and general matings [114]. The experimental results showed the relative good performances of DPLL.…”

Section: Non-clausal Reasoningmentioning

confidence: 99%

“…In the seminal work by N. Murray [151], propositional and FOL NC Resolution was defined in a combined functional and classical manner and has been applied to different operating contexts, e.g. [15,180]. Each proper NC Resolution inference is followed by some functional-logical simplifications of the formula.…”

Section: Quantified Booleanmentioning

confidence: 99%

The Horn Non-Clausal Class and its Polynomiality

Imaz¹

2021

Preprint

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The expressiveness of propositional non-clausal (NC) formulas is exponentially richer than that of clausal formulas. Yet, clausal efficiency outperforms non-clausal one. Indeed, a major weakness of the latter is that, while Horn clausal formulas, along with Horn algorithms, are crucial for the high efficiency of clausal reasoning, no Horn-like formulas in non-clausal form had been proposed.To overcome such weakness, we define the hybrid class H NC of Horn Non-Clausal (Horn-NC) formulas, by adequately lifting the Horn pattern to NC form, and argue that H NC , along with future Horn-NC algorithms, shall increase non-clausal efficiency just as the Horn class has increased clausal efficiency.Secondly, we: (i) give the compact, inductive definition of H NC ; (ii) prove that syntactically H NC subsumes the Horn class but semantically both classes are equivalent, and (iii) characterize the non-clausal formulas belonging to H NC .Thirdly, we define the Non-Clausal Unit-Resolution calculus, UR NC , and prove that it checks the satisfiability of H NC in polynomial time. This fact, to our knowledge, makes H NC the first characterized polynomial class in NC reasoning.Finally, we prove that H NC is linearly recognizable, and also that it is both strictly succincter and exponentially richer than the Horn class.We discuss that in NC automated reasoning, e.g. satisfiability solving, theorem proving, logic programming, etc., can directly benefit from H NC and UR NC and that, as a by-product of its proved properties, H NC arises as a new alternative to analyze Horn functions and implication systems.

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“…To deal with sets of general formulas which can describe complex problems naturally, generalized resolution principle has been put forward for Boolean logic and many-valued logic as well, see [16][17][18][19][20][21], among others. In generalized resolution, the concept of literal is extended to generalized literal (which is composed by atomic formulas, 0, 1 and logical connectives), the resolvents can be obtained not only by the complementary literals from two conventional clauses, but also atomic formulas from any generalized clauses.…”

Section: Introductionmentioning

confidence: 99%

Non-Clausal Multi-ary α-Generalized Resolution Calculus for a Finite Lattice-Valued Logic

Xu¹,

Li²,

He³

et al. 2018

IJCIS

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Due to the need of the logical foundation for uncertain information processing, development of efficient automated reasoning system based on non-classical logics is always an active research area. The present paper focuses on the resolution-based automated reasoning theory in a many-valued logic with truth-values defined in a lattice-ordered many-valued algebraic structure -lattice implication algebras (LIA). Specifically, as a continuation and extension of the established work on binary resolution at a certain truth-value level α (called α-resolution), a non-clausal multi-ary α-generalized resolution calculus is introduced for a lattice-valued propositional logic LP(X) based on LIA, which is essentially a non-clausal generalized resolution avoiding reduction to normal clausal form. The new resolution calculus in LP(X) is then proved to be sound and complete. The concepts and theoretical results are further extended and established in the corresponding lattice-valued first-order logic LF(X) based on LIA.

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Non-clausal reasoning with propositional definite theories

Cited by 6 publications

References 7 publications

α-Generalized lock resolution method in linguistic truth-valued lattice-valued logic

α-Generalized lock resolution method in linguistic truth-valued lattice-valued logic

The Horn Non-Clausal Class and its Polynomiality

Non-Clausal Multi-ary α-Generalized Resolution Calculus for a Finite Lattice-Valued Logic

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