Compiled Labelled Deductive Systems: A Uniform Presentation of Non-classical LogicsResearch Studies Press, 2004 - 343 páginas This book introduces a general framework, called Compiled Labelled Deductive System (CLDS), for a unified presentation of logics. It shows how this technique is applied to various families of non-classical logics widely used in Computer Science and Artificial Intelligence. It includes complete natural deduction proof systems, together with proofs and examples, for the families of propositional and predicate modal logics, propositional conditional logics of normality, multiplicative linear logic and for Lukasiewicz fuzzy logic. The CLDS framework generalises the notion of a logical theory to a structured theory consisting of labelled formulas and relations between the labels. This formalisation makes the logics more amenable to applications. Moreover, the framework provides a semantic approach based on a first-order translation, which can be uniformly applied to any logic whose semantics is first-order axiomatisable. Such a semantic approach also facilitates the development of automated theorem provers for non-classical logics. |
Conteúdo
82 | 3 |
Introduction | 37 |
Derivability and Semantic Entailment | 88 |
Direitos autorais | |
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Termos e frases comuns
accessibility relation Add minus sign arbitrary assumptions axiom schemas axiomatic system axiomatisation binary boxa C₁ classical logic CLDS Cmce conditional logic constant symbols declarative term declarative unit defined denoted derivability relation ECLDS system exists Ext(LM extended algebra FCLDS finite first-order logic first-order translation formalisation FOT(C FOT(Cmcc Func(LM function symbols fuzzy logic ground term Hence inference rules initial configuration instantiation K8-MLDS Kripke semantic labelling algebra labelling language LCLDS LDCL system Lemma linear logic logic of elsewhere logic of normality Lukasiewicz fuzzy logic M(Cmcc maximal consistent configuration MLDSs modal formula modal operators modal theory natural deduction natural deduction system normal modal logics possible worlds proof system proof theory properties propositional MLDS propositional modal proved quantified modal language R-literals R(Wo satisfiability semantic entailment semantic structure sign to read sound and complete strict box substructural logic syntactic Theorem variable w₁ wffs