We show that simultaneous rigid E-uniication, or SREU for short, is decidable and in fact EXPTIME-complete in the case of one variable. This result implies that the 8 98 fragment of intuitionistic logic with equality is decidable. Together with a previous result regarding the undecidability of the 99-fragment, we obtain a complete classiication of decidability of the prenex fragment of intuitio...

We show that simultaneous rigid E-uniication, or SREU for short, is decidable and in fact EXPTIME-complete in the case of one variable. This result implies that the 8 98 fragment of intuitionistic logic with equality is decidable. Together with a previous result regarding the undecidability of the 99-fragment, we obtain a complete classiication of decidability of the prenex fragment of intuitio...

In order to represent, compute and reason with advanced data types one must go beyond the traditional treatment of data types as being inductive types and, instead, consider them as inductive families. Strictly positive types (SPTs) form a grammar for defining inductive types and, consequently, a fundamental question in the the theory of inductive families is what constitutes a corresponding gr...

We show that simultaneous rigid E-uni cation, or SREU for short, is decidable and in fact EXPTIME-complete in the case of one variable. This result implies that the 8 98 fragment of intuitionistic logic with equality is decidable. Together with a previous result regarding the undecidability of the 99-fragment, we obtain a complete classi cation of decidability of the prenex fragment of intuitio...

The presentation will contrast the complexity results for proving assertions in classical and intuitionistic logic. The comparison will be built upon the known results for propositional logic and predicate one. The predicate case will be based upon the Mints hierarchy in intuitionistic logic which will be contrasted with its counterpart i.e. the prenex hierarchy in classical logic. The di erenc...

We show that simultaneous rigid E-uni cation, or SREU for short, is decidable and in fact EXPTIME-complete in the case of one variable. This result implies that the 8 98 fragment of intuitionistic logic with equality is decidable. Together with a previous result regarding the undecidability of the 99-fragment, we obtain a complete classi cation of decidability of the prenex fragment of intuitio...

A minimal theorem in a logic L is an L-theorem which is not a nontrivial substitution instance of another L-theorem. Komori (1987) raised the question whether every minimal impli-cational theorem in intuitionistic logic has a unique normal proof in the natural deduction system NJ. The answer has been known to be partially positive and generally negative. It is shown here that a minimal implicat...