Representation Theorems and Theorem Proving in Non-Classical Logics
نویسنده
چکیده
In this paper we present a method for automated theorem proving in non-classical logics having as algebraic models bounded distributive lattices with certain types of operators. The idea is to use a Priestley-style representation for distributive lattices with operators in order to define a class of Kripke-style models with respect to which the logic is sound and complete. If this class of Kripke-style models is elementary, it can then be used for a translation to clause form; satisfiability of the resulting clauses can be checked by resolution. We illustrate the ideas by several examples.
منابع مشابه
representation theorems of $L-$subsets and $L-$families on complete residuated lattice
In this paper, our purpose is twofold. Firstly, the tensor andresiduum operations on $L-$nested systems are introduced under thecondition of complete residuated lattice. Then we show that$L-$nested systems form a complete residuated lattice, which isprecisely the classical isomorphic object of complete residuatedpower set lattice. Thus the new representation theorem of$L-$subsets on complete re...
متن کاملTPTP and Beyond: Representation of Quantified Non-Classical Logics
The practical employment of automated deduction systems requires the user to input problem statements in a well-formed string representation. While this presentation is usually fixed by the respective system, the various language dialects of the TPTP library are meanwhile accepted as a de-facto standard for all current automated theorem provers based on classical logics. In the context of reaso...
متن کاملTruth Values and Connectives in Some Non-Classical Logics
The question as to whether the propositional logic of Heyting, which was a formalization of Brouwer's intuitionistic logic, is finitely many valued or not, was open for a while (the question was asked by Hahn). Kurt Gödel (1932) introduced an infinite decreasing chain of intermediate logics, which are known nowadays as Gödel logics, for showing that the intuitionistic logic is not finitely (man...
متن کاملAutomated Theorem Proving in aSimple
Higher-order representation techniques allow elegant encod-ings of logics and programming languages in the logical framework LF, but unfortunately they are fundamentally incompatible with induction principles needed to reason about them. In this paper we develop a meta-logic M2 which allows inductive reasoning over LF encodings, and describe its implementation in Twelf, a special-purpose automa...
متن کاملAutomated Theorem Proving in a Simple Meta-Logic for LF
Higher-order representation techniques allow elegant encodings of logics and programming languages in the logical framework LF, but unfortunately they are fundamentally incompatible with induction principles needed to reason about them. In this paper we develop a meta-logic M2 which allows inductive reasoning over such LF encodings, and describe its implementation in Twelf, a special-purpose au...
متن کامل