Completeness of the ZH-calculus

Expressive Completeness of Duration Calculus

This paper compares the expressive power of first-order monadic logic of order, a fundamental formalism in mathematical logic and the theory of computation, with that of the Propositional version of Duration Calculus (PDC), a formalism for the specification of realtime systems. Our results show that the propositional duration calculus is expressively complete for first-order monadic logic of or...

Completeness of Continuation Models for lm-Calculus

We show that a certain simple call-by-name continuation semantics of Parigot’s λμ-calculus is complete. More precisely, for every λμ-theory we construct a cartesian closed category such that the ensuing continuation-style interpretation of λμ, which maps terms to functions sending abstract continuations to responses, is full and faithful. Thus, any λμ-category in the sense of L. Ong (1996, in “...

L-Completeness of the Lambek Calculus with the Reversal Operation

In this paper we prove that the Lambek calculus allowing empty antecedents and enriched with a unary connective corresponding to language reversal is complete with respect to the class of models on subsets of free monoids (L-models). 1 The Lambek Calculus with the Reversal Operation We consider the calculus L, introduced in [4]. The set Pr = {p1, p2, p3, . . . } is called the set of primitive t...

The Completeness of the First-Order Functional Calculus

Duality and the Completeness of the Modal mu-Calculus

We consider the modal-calculus due to Kozen, which is a nitary modal logic with least and greatest xed points of monotone operators. We extend the existing duality between the category of modal algebras with homomorphisms and the category of descriptive modal frames with contractions to the case of having xed point operators. As a corollary, we obtain completeness results for two proof systems ...