Meta-theory of first-order predicate logic
نویسنده
چکیده
We present a formalization of parts of Melvin Fitting’s book “FirstOrder Logic and Automated Theorem Proving” [1]. The formalization covers the syntax of first-order logic, its semantics, the model existence theorem, a natural deduction proof calculus together with a proof of correctness and completeness, as well as the Löwenheim-Skolem theorem.
منابع مشابه
A semantic study of the first-order predicate logic with uncertainty involved
In this paper, we provide a semantic study of the first-order predicate logic for situations involving uncertainty. We introduce the concepts of uncertain predicate proposition, uncertain predicate formula, uncertain interpretation and degree of truth in the framework of uncertainty theory. Compared with classical predicate formula taking true value in {0, 1}, the degree of truth of uncertain p...
متن کاملA Compact Argumentation System for Agent System Specification
We present a non-monotonic logic tailored for specifying compact autonomous agent systems. The language is a consistent instantiation of a logic based argumentation system extended with Brooks’ subsumption concept and varying degree of belief. Particulary, we present a practical implementation of the language by developing a meta-encoding method that translates logical specifications into compa...
متن کاملFrom Logic Programming Semantics to the Consistency of Syntactical Treatments of Knowledge and Belief
This paper concerns formal theories for reasoning about the knowledge and belief of agents. It has seemed attractive to researchers in artificial intelligence to formalise these propositional attitudes as predicates of first-order predicate logic. This allows the agents to express stronger introspective beliefs and engage in stronger meta-reasoning than in the classical modal operator approach....
متن کاملCombining Hilbert Style and Semantic Reasoning in a Resolution Framework
Proceedings of CADE-15, LNAI 1421, pp. 205–219, 1998 Many non-classical logics can be axiomatized by means of Hilbert Systems. Reasoning in Hilbert Systems, however, is extremely inefficient. Most inference methods therefore use the semantics of a logic in one kind or another to get more efficiency. In this paper a combination of Hilbert style and semantic reasoning is proposed. It is particula...
متن کاملOn the Relationship between Description Logic-based and F-Logic-based Ontologies
Many popular ontology languages are based on (subsets of) first-order predicate logic, with classes represented by unary predicates and properties by binary predicates. Specifically, the Semantic Web ontology language OWL DL is based on the Description Logic SHOIN . F-Logic is an ontology language which is also based on first-order logic, but classes and properties are modeled as terms rather t...
متن کامل