In this paper we study proofs of some general forms of the Second Incompleteness Theorem. These forms conform to the Feferman format, where the proof predicate is fixed and the representation of the axiom set varies. We ...
In this paper we study Jointed Branching Time Structures equipped with a chrono-function that assigns times to moments. We develop a collection of examples of such structures in a systematic way. We use our systematic ...
In 1992 Dyckhoff developed a sequent calculus for intuitionistic propositional logic in which proof search is terminating. In this paper this result is extended to several intuitionistic modal logics, including intuitionistic ...
General conditions on sequent calculi are formulated under which the intermediate and modal logics corresponding to the calculi have uniform interpolation. It follows that the intuitionistic versions of K and KD, as well ...
In recent years, the logic of questions and dependencies has been investigated in the closely related frameworks of inquisitive logic and dependence logic. These investigations have assumed classical logic as the background ...
In this paper we prove that three of the main propositional logics of dependence (including propositional dependence logic and inquisitive logic), none of which is structural, are structurally complete with respect to a ...
It is shown that no intermediate predicate logic that is sound and complete with respect to a class of frames, admits a strict alternative Skolemization method. In particular, this holds for intuitionistic predicate logic ...
This paper develops the philosophy and technology needed for adding a supremum operator to the interpretability logic ILM of Peano Arithmetic (PA). It is wellknown that any theories extending PA have a supremum in the ...
In this paper we study Robinson’s Arithmetic Q. We prove a basic result that says that, in a sense explained in the paper, Q can be split into two parts. We prove some consequences of this result. (i) Q is not a poly-pair ...
A new logic is presented without predicates-except equality. Yet its expressive power is the same as that of predicate logic, and relations can faithfully be represented in it. In this logic we also develop an alternative ...
This note consists of a collection of observations on the notion of simplicity in the setting of proofs. It discusses its properties under formalization and its relation to the length of proofs, showing that in certain ...
A method is presented that connects the existence of uniform interpolants to the existence of certain sequent calculi. This method is applied to several modal logics and is shown to cover known results from the literature, ...
In the context of Elementary Arithmetic (EA) we know that already an extremely weak arithmetical theory like R proves every true Σ1-sentence. Thus, it would seem that adding the true Σ1-sentences to the axiom set of a given ...
An alternative Skolemization method, which removes strong quantifiers from formulas, is presented that is sound and complete with respect to intermediate predicate logics of finite width. For logics without constant domains ...
Rybakov (1984) proved that the admissible rules of IPC are decidable. We give a proof of the same theorem, using the same core idea, but couched in the many notions that have been developed in the mean time. In particular, ...
Friedman, Harvey M.; Visser, Albert(Department of Philosophy of Utrecht Universityhttp://phil.uu.nl/preprints/lgps/, 2014-01-03)
Two salient notions of sameness of theories are synonymy, aka definitional equivalence, and bi-interpretability. Of these two definitional equivalence is the strictest notion. In which cases can we infer synonymy from ...
Halbach, Volker; Visser, Albert(Department of Philosophy of Utrecht Universityhttp://phil.uu.nl/preprints/lgps/, 2014-01-03)
In this paper we discuss Henkin's question concerning a formula that has been described as expressing its own provability. We analyze Henkin's formulation of the question and the early responses by Kreisel and Löb and ...
Visser, Albert(Department of Philosophy of Utrecht Universityhttp://phil.uu.nl/preprints/lgps/, 2014-01-10)
In this paper we study a new relation between sentences: the jump relation. The idea of the jump relation is based on an analysis of Feferman's Theorem that the inconsistency of a theory U is interpretable over U. The jump ...