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This paper is focused on α-generalized semantic resolution automated reasoning method in linguistic truth-valued lattice-valued propositional logic. ... The Presented work provides some foundations for resolution-based automated reasoning in linguistic truth-valued lattice-valued logic based on lattice implication algebra. ... Like Robinson's resolution principle, the semantic resolution method is also sound and complete in predicate logic. ...doi:10.1080/18756891.2013.857895 fatcat:w33t5slio5ervkmnmd67cri7xq
This paper focuses on multi-ary α-semantic resolution automated reasoning method based on multi-ary α-resolution principle for lattice-valued propositional logic LP(X) with truth-value in lattice implication ... The definitions of the multi-ary α-semantic resolution and multi-ary α-semantic resolution deduction in lattice-valued propositional logic LP(X) are given, respectively, and the soundness and completeness ... In this section, the multi-ary α-semantic resolution method in lattice-valued propositional logic LP(X) will be investigated based on the multi-ary α-resolution principle which has been listed in Section ...doi:10.24507/ijicic.12.05.1629 fatcat:vqgpbipvkbdrnmfsgmptjlbcim
Lecture Notes in Computer Science
In the propositional case, a representational language L, defined by a set of propositional variables V ar and logical connectives f 0 , . . . , f n , can be viewed as a term algebra (or Lindenbaum's algebra ... The lattice K P , ≤ is a convenient tool to discuss the scope of the resolution method defined in terms of resolution algebras: if P is a resolution logic, then so are all the logics in K P . ...doi:10.1007/978-3-540-30210-0_2 fatcat:vzlccfeqijg3tfh3v73lelk7du
Based on the general form of -resolution principle for a lattice-valued logic with truth-values defined in a latticevalued logical algebra structure -lattice implication algebra, the further extended - ... Firstly, -quasi-lock semantic resolution method in lattice-valued propositional logic LP(X) is established by combining the lock and semantic resolution simultaneously, and its theorems of soundness and ... The proposition algebra of the lattice-valued proposition calculus on the set X of propositional variables is the free T algebra on X and denoted by LP(X). 3 . 3 -Quasi-Lock Semantic Resolution for Lattice-Valued ...doi:10.1080/18756891.2013.859868 fatcat:qf3kulc4gvgnrlfpmcw4vdi244
In this paper we propose a resolution proof framework on the basis of which automated proof systems for finitely -valued first-order logics (F FO logics) can be introduced and studied. ... \Ve define the notion of a first-order resolution proof system and we show that for every disjunctive F FO logic a refutationally complete resolution proof system can be constructed. ... O'Hearn was supported in part by a Natural Sciences and Engineering Research Council of Canada Postgraduate Scholarship. ...doi:10.1016/s0747-7171(10)80002-1 fatcat:uiicseul3vf5jk6psgzcje5ode
We review the conceptual foundations of inquisitive semantics, introduce the propositional system, discuss its relations with classical, intuitionistic, and dependence logic, and describe an important ... This paper provides a concise survey of a body of recent work on propositional inquisitive logic. ... In the propositional setting, an information state is construed as a set of propositional valuations. ...doaj:143ad9a6c1d14f719873885b37272c96 fatcat:okm774banjcf3bbejls3uokeoa
In this paper, an α-resolution method for a set of lattice-valued Horn generalized clauses is established in lattice-valued propositional logic system L P(X) based on lattice implication algebra. ... It indicates the reasoning rules in a resolution process, which aims at deleting α-resolution literals and obtaining a resolvent. ... Preliminaries In this section we review some essential conceptions about lattice implication algebra, α-resolution principle based on lattice-valued propositional logic system L P(X). ...doi:10.1080/18756891.2015.1129580 fatcat:t6u5skct2bftxeptv3hs6hlrxq
propositional logical system, namely, syntax, semantics, and proof theory. ... By seeing “formulas as relations”, relational logic devel- oped in terms of certain algebras of relations. ...
However, this principle can be encoded differently, i.e., in different logical-algebraic objects. ... propositions in such a semantics. ... this semantics, the valuation relation (2) is not a total function. ...arXiv:1904.01364v1 fatcat:f66kgovjjzf2fondcm33jyeqdu
We present a resolution-based proof method for finite-valued propositional logics based on an algorithmic reduction procedure that expresses these logics in terms of bivalent semantics. ... Thus, differently from the approaches in [1,7], unification on labels can be easily seen as equivalent to the ordinary application of classical propositional resolution. ... The very language S may be seen as a Σ-algebra, if we take V " S: this defines the so-called term algebra generated by the variables in A over the propositional signature Σ. ...doi:10.1016/j.entcs.2016.09.001 fatcat:knq57n63gvg6rkdxe6c7s35ozy
In the first case, C. C. Chang’s MV-algebras serve as algebraic models, and in the second case we use MV,,-algebras defined by the author. ... 88e:()3033 the study of free algebras in the class of algebraic (matrix) models of a given logical calculus and the use of the characterization of so-called Lindenbaum algebras. ...
But the semantics relies on a three-valued truth valuation first suggested by de Finetti. ... The analysis of a notion of consistency of a set of conditional objects is studied in the light of such a three-valued semantics and higher level counterparts of the deduction theorem, modus ponens, resolution ...
of the Human law, but can be, in principle, applied to several other questions in philosophical logic. ... The algebra of truth values in this case is isomorphic to standard three-valued propositional logic. ...
The exposition remains elementary and does not presuppose any previous knowledge or familiarity with the algebraic approach to logic. ... The second motivation is methodological: the present treatment aims at highlighting the algebraic and order-theoretic nature of the correspondence mechanism. ... The connections between the algebraic and the relational semantics of modal logic and other propositional logics form a mathematically rich and deep theory, the foundations of which were laid by Stone ...arXiv:1606.06881v1 fatcat:hpwcoofjlne2lhjbuclntgkkxi
Based on the extensive work of α-resolution automated reasoning in linguistic truth-valued lattice-valued logic, this paper discusses the structure and its α-resolvability of the generalized literal. ... Automatic reasoning is a very challenging research area in the field of artificial intelligence. ... Similarly, the truth-valued domain of L n P(X) is a Łukasiewicz implication algebra L n . Definition 6 (see  ). A valuation of LP(X) is a propositional algebra homomorphism c: LP(X) ⟶ L. ...doi:10.1155/2022/2677457 fatcat:dxqcre3fy5h4bfobacrzihvn4i
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