We prove in HOL that three proof systems for classical rst-order predicate logic, the Hilbertian axiomatization, the system of natural deduction, and a variant of sequent calculus, are isomorphic. The isomorphism is in the sense that provability of a conclusion from hypotheses in one of these proof systems is equivalent to provability of this conclusion from the same hypotheses in the others. P...

Inference rules in the sequent calculus can be interpreted as both proof construction rules and proof search rules. However, the kind of information used in each case is somewhat different. In this paper we explore these differences by using a multiple-conclusioned sequent calculus for intuitionistic logic (LM) as a search calculus for proofs in the single-conclusioned intuitionistic sequent ca...

We introduce a sequent calculus for the temporal-over-topological fragment DTL ◦∗/2 0 of dynamic topological logic DTL, prove soundness semantically, and prove completeness syntactically using the axiomatization of DTL ◦∗/2 0 given in [3]. A cut-free sequent calculus for DTL ◦∗/2 0 is obtained as the union of the propositional fragment of Gentzen’s classical sequent calculus, two 2 structural r...

In this paper we argue that sequent proofs systems are a better deductive apparatus for introducing proofs to students than are natural deduction systems. Natural deduction derivations of superintuitionistic theorems (theorems of classical logic that are not intuitionistically valid) require indirect and often obtuse constructions. Constructing derivations in sequent systems is uniform, driven ...

Stilling basins are designed to reduce the high kinetic energy of supercritical flow in a downstream spillway. The USBR II stilling basin is distinguished by chute blocks fixed at upstream end and dented sill end, allowing for effective dissipation excess energy. This research investigates effect chute-block geometry on hydraulic performance basin. Six modified chute-blocks with identical dimen...

We present a sequent calculus that allows to abstract over a type variable. The introduction of the abstraction on the right-hand side of a sequent corresponds to the universal quantification; whereas, the introduction of the abstraction on the lefthand side of a sequent corresponds to the existential quantification. The calculus provides a correspondence with second-order classical proposition...

This paper is concerned with the study of the number of proofs of a sequent in the commutative Lambek calculus. We show that in order to count how many different proofs in βη-normal form a given sequent Γ ` α has, it suffices to enumerate all the ∆ ` β which are “minimal”, such that Γ ` α is a substitution instance of ∆ ` β. As a corollary we obtain van Benthem’s finiteness theorem for the Lamb...

System SKS is a set of rules for classical propositional logic presented in the calculus of structures. Like sequent systems and unlike natural deduction systems, it has an explicit cut rule, which is admissible. In contrast to sequent systems, the cut rule can easily be restricted to atoms. This allows for a very simple cut elimination procedure based on plugging in parts of a proof, like norm...

We investigate observation logic, an intuitionnistic modal logic designed for reasoning about approximation and multiple contexts, and propose a sequent-calculus formulation of this logic. Due to the validy of an axiom (called T2) which is a weakening of T, one needs an adaptation of the usual sequent-calculus formalism in order to have some classical properties of sequent calculus, such as cut...

Sequent automaton is an intermediate abstract model used on the way from representation of a desired behavior of some engineering system at the algorithmic level to the detailed description of a logical control device designed to provide this behavior, in terms of logic circuits. In this paper, there are regarded the problems of obtaining a sequent automaton from the preceding model of parallel...