The Logical Strength of Büchi's Decidability Theorem

A Logical Approach to Decidability of Hierarchies of Regular Star-Free Languages

We propose a new, logical, approach to the decidability problem for the Straubing and Brzozowski hierarchies based on the preservation theorems from model theory, on a theorem of Higman, and on the Rabin tree theorem. In this way, we get purely logical, short proofs for some known facts on decidability, which might be of methodological interest. Our approach is also applicable to some other sim...

On the Strength of Proof-Irrelevant Type Theories

We present a type theory with some proof-irrelevance built into the conversion rule. We argue that this feature is useful when type theory is used as the logical formalism underlying a theorem prover. We also show a close relation with the subset types of the theory of PVS. We show that in these theories, because of the additional extentionality, the axiom of choice implies the decidability of ...

Algebraic and Model Theoretic Techniques for Fusion Decidability in Modal Logics

We introduce a new method (derived from model theoretic general combination procedures in automated deduction) for proving fusion decidability in modal systems. We apply it to show fusion decidability in case not only the boolean connectives, but also a universal modality and nominals are shared symbols.

Decidability, Undecidability, and Gödel's Incompleteness in Relativity Theories

In this paper we investigate the logical decidability and undecidability properties of relativity theories. To this end, we need to recall versions of relativity theory which are built up in a logical framework i.e. which are theories in the sense of mathematical logic (section 2). In Part I (section 3) we investigate decidability properties of versions of relativity. We will find that the answ...

Decidability and Tameness in the Theory of Finite Semigroups