Automata theory approach to predicate intuitionistic logic

Automata Theory Approach to Predicate Intuitionistic Logic

Predicate intuitionistic logic is a well established fragment of dependent types. According to the Curry-Howard isomorphism proof construction in the logic corresponds well to synthesis of a program the type of which is a given formula. We present a model of automata that can handle proof construction in full intuitionistic first-order logic. The automata are constructed in such a way that any ...

Interpolation theorems for intuitionistic predicate logic

Craig interpolation theorem (which holds for intuitionistic logic) implies that the derivability of X,X’-¿Y’ implies existence of an interpolant I in the common language of X and X’-¿Y’ such that both X-¿I and I,X’-¿Y’ are derivable. For classical logic this extends to X,X’-¿Y,Y’, but for intuitionistic logic there are counterexamples. There is a version true for intuitionistic propositional (b...

Predicate Logic and Tree Automata with Tests

Using Tree Automata to Investigate Intuitionistic Propositional Logic

Intuitionistic logic is an important variant of classical logic, but it is not as well-understood, even in the propositional case. In this thesis, we describe a faithful representation of intuitionistic propositional formulas as tree automata. This representation permits a number of consequences, including a characterization theorem for free Heyting algebras, which are the intutionistic analogu...

Meta-theory of first-order predicate logic

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.