In this paper, we address the problem of defining a fixpoint semantics for Constraint Handling Rules (CHR) that captures the behavior of both simplification and propagation rules in a sound and complete way with respect to their declarative semantics. Firstly, we show that the logical reading of states with respect to a set of simplification rules can be characterized by a least fixpoint over t...

We introduce model-theoretic semantics [6] for Higher-Order Horn logic programming language. One advantage of logic programs over conventional non-logic programs has been that the least fixpoint is equal to the least model, therefore it is associated to logical consequence and has a meaningful declarative interpretation. In simple theory of types [9] on which Higher-Order Horn logic programming...

We introduce PHFL, a probabilistic extension of higher-order fixpoint logic, which can also be regarded as temporal logics such PCTL and the $\mu^p$-calculus. show that PHFL is strictly more expressive than $\mu^p$-calculus, model-checking problem for finite Markov chains undecidable even $\mu$-only, order-1 fragment PHFL. Furthermore full far expressive: we give translation from Lubarsky's $\m...

Algebraical fixpoint theory is an invaluable instrument for studying semantics of logics. For example, all major semantics of logic programming, autoepistemic logic, default logic and more recently, abstract argumentation have been shown to be induced by the different types of fixpoints defined in approximation fixpoint theory (AFT). In this paper, we add a new type of fixpoint to AFT: a ground...

Nominal sets provide a framework to study key notions of syntax and semantics such as fresh names, variable binding and α-equivalence on a conveniently abstract categorical level. Coalgebras for endofunctors on nominal sets model, e.g., various forms of automata with names as well as infinite terms with variable binding operators (such as λ-abstraction). Here, we first study the behaviour of or...

This paper presents a method for computing a least fixpoint of a system of equations over booleans. The resulting computation can be significantly shorter than the result of iteratively evaluating the entire system until a fixpoint is reached.

We propose an axiomatization of fixpoint operators in typed call-by-value programming languages, and give its justifications in two ways. First, it is shown to be sound and complete for the notion of uniform T -fixpoint operators of Simpson and Plotkin. Second, the axioms precisely account for Filinski’s fixpoint operator derived from an iterator (infinite loop constructor) in the presence of f...