A predicate language over a propositional language S is a couple qS = ( S , q ) where q is the signature of qS , i.e. the function which divides descriptive terms D ( q ) of qS into syntactical categories. All predicate languages involve the sets V f and V b of free and bound ...
Logic: study of entailment relations Using Logic# No universal language / semantics No universal reasoning scheme Start with first-order predicate calculus(FOL) Why do we need formal Knowledge Representation?# Natural languages exhibit ambiguity ambiguity make it difficult to make any inferences Syntax ...
Truth in First-order Logic Sentences are true with respect to a model and an interpretation Model contains 1 objects (domain elements) and relations among them Interpretation specifies referents for Constant symbols -> objects Predicate symbols -> relations Function symbols -> functional relations ...
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We give a sequential reduction technique for transforming a formula of the pure predicate calculus to a sequence of 'increasingly accurate' propositional logic 'approximations' to the predicate formula. At each stage of approximation, one of the following three cases occurs: (1) the approximation sh...
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This new perspective, combined with much improved insights into the semantically defined discourse dependency of natural language sentences, leads to a novel and more functionally oriented approach to logic and to a reappraisal of traditional predicate calculus, whose main fault, undue existential import...
Propositional and Predicate Logicdoi:10.1007/978-3-319-64021-1_6Propositional logic is the study of propositions, where a proposition is a statement that is either true or false. Propositional logic may be used to encode simple arguments that are expressed in...Gerard O'ReganSQC Consulting...
Propositional and predicate logics of incomplete informationdoi:10.1016/J.ARTINT.2021.103603Marco ConsolePaolo GuagliardoLeonid LibkinElsevier
Propositional logic may be used to encode simple arguments that are expressed in natural language, and to determine their validity. The validity of an argument may be determined from truth tables, or using the inference rules such as modus ponens to establish the conclusion. Predicate logic allows...