We establish the strictness of several set quantiVer alternation hierarchies that are based on modal logic, evaluated on various classes of Vnite graphs. This extends to the modal setting a celebrated result of Matz, Schweikardt and Thomas (2002), which states that the analogous hierarchy of monadic second-order logic is strict. Thereby, the present paper settles a question raised by van Benthe...

We propose a relaxation of Kleene algebra by giving up strictness and right-distributivity of composition. This allows the subsumption of Dijkstra’s computation calculus, Cohen’s omega algebra and von Wright’s demonic refinement algebra. Moreover, by adding domain and codomain operators we can also incorporate modal operators. Finally, it is shown that the predicate transformers form lazy Kleen...

This article deals with the interrelation of deontic operators in contracts – an aspect often neglected when considering only one of the involved parties. On top of an automata-based semantics we formalise the onuses that obligations, permissions and prohibitions on one party impose on the other. Such formalisation allows for a clean notion of contract strictness and a derived notion of contrac...

The minimal function graph semantics of Jones and Mycroft is a standard denotational semantics modified to include only ‘reachable’ parts of a program. We show that it may be expressed directly in terms of the standard semantics without the need for instrumentation at the expression level and, in doing so, bring out a connection with strictness. This also makes it possible to prove a stronger t...

The attribute dependence graph of a syntax tree may be partitioned into disjoint regions. Attribute instances in di€erent regions are independent of one other. The advantages of partitioning the attribute dependence graph include simplifying the attribute grammar conceptually and allowing the possibility of parallel evaluation. We present a static partitioning algorithm for attribute grammars. ...

This paper proves the confluency and the strong normalizability of the call-by-value λμcalculus with the domain-free style. The confluency of the system is proved by improving the parallel reduction method of Baba, Hirokawa and Fujita. The strong normalizability is proved by using the modified CPS-translation, which preserves the typability and the reduction relation. This paper defines the cla...

Due to strictness problems, usually the syntactical definition of Frege structures is conceived as a truth theory for total applicative theories. To investigate Frege structures in a partial framework we can follow two ways. First, simply by ignoring undefinedness in the truth definition. Second, by introducing of a certain notion of pointer. Both approaches are compatible with the traditional ...

We present a simple and workable axiomatization of domain theory within intuitionistic set theory, in which predomains are (special) sets, and domains are algebras for a simple equational theory. We use the axioms to construct a relationally parametric set-theoretic model for a compact but powerful polymorphic programming language, given by a novel extension of intuitionistic linear type theory...