The need for more expressive systems of knowledge representation is not controversial although it is still debatable whether or not such systems have to be based on formal logic. In this book the author takes it as read that the formal approach is a worthy one. The objective is to explore the development of formal languages and appropriate logics for that aspect of knowledge representation concerned with reasoning about truth and modality. Much of this work is based upon the theories of modality and truth which were developed in the period 1960-1980. There has been a great deal of activity within the logical community centred upon the development of logics of truth and modality and the objective is to bring this material to the attention of AI researchers by putting it in a context where it might be directly applicable to AI knowledge representation. The book introduces various logics of truth and modality as part of a foundation for the construction of theories of knowledge representation.
It reviews the various semantic theories of truth which seek to come to terms with the constraints imposed by the semantic and logical paradoxes and in particular the theories of Kripke, Gupta, Herzberger, Gilmore, Aczel and Feferman are discussed.
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
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Maße
Höhe: 246 mm
Breite: 175 mm
Gewicht
ISBN-13
978-0-273-03186-4 (9780273031864)
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Schweitzer Klassifikation
Part 1 Reasoning agents: modality and knmowledge representation; propositions and modality; possible worlds; higher-order modal logic; "fine-grained" propositions; propositions as primitive; higher-order theories and computational tractability; propositions as senetneces; syntactic modality; representationalism; theories of truth, modality and propositions. Part 2 Truth and paradox: the Lambda calculus; models and semantics of the Lambda calculus; the predicate calculus; the Tarski Bioconditionals; logics of truth. Part 3 Truth through fixpoints: Kleene strong three-values logic as a theory of truth and falsity; models of KFG; a reformulation; truth, falsity and propostions; FKG as a modal theory; the strengthened liar. Part 4 Stable truth: the Gupta-Herzberger Semantic Theory; logics of stable truth; a weak modal logic of truth; stable axioms and necessittion; the T-axiom; the S4-axiom; the S5-axiom; a further non-standard principle; some consequences; the "liar" and the "truth teller". Part 5 Frege structures: the language of Frege structures; models in TP; properties and relations; natural language semantics; undefinability results. Part 6 Modal logic: the language; possible world semantics; modal logics. part 7 Truth in modal logic: modal fixpoints; modality and stability; a theory pf propositions, truth and modality. Part 8 Predicative modality: the language; intensional paradox; a trnaslation between L5 and L3; logics of truth and modality with and without full necessitaiton; logicals of truth, propostions and modality. Part 9 Conclusions: logics of truth; modality.
