Over the last years several new approaches for modeling situations, actions, and causality within a deductive framework were proposed. These new approaches treat the facts about a situation as resources, which are consumed and produced by actions. In this paper we extend one of these approaches, viz. an equational logic approach, by reifying actions to become resources as well. Using the concep...

Although functional as well as logic languages use equality to discriminate between logically different cases, the operational meaning of equality is different in such languages. Functional languages reduce equational expressions to their Boolean values, True or False, logic languages use unification to check the validity only and fail otherwise. Consequently, the language Curry, which amalgama...

A sound and complete approach for encoding the action description language A developed by M. Gelfond and V. Lifschitz in an equational logic program is given. Our results allow the comparison of the resource-oriented equational logic based approach and various other methods designed for reasoning about actions, most of them based on variants of the situation calculus, which were also related to...

Equational theories underly many elds of computing, including functional programming, symbolic algebra, theorem proving, term rewriting and constraint solving. In this paper we show a method for implementing many equational theories with a limited class of logic programs. We de ne regular equational theories, a useful class of theories, and illustrate with a number of examples how our method ca...

In Floyd-Hoare logic, programs are dynamic while assertions are static (hold at states). In action logic the two notions become one, with programs viewed as on-the-fly assertions whose truth is evaluated along intervals instead of at states. Action logic is an equational theory ACT conservatively extending the equational theory REG of regular expressions with operations preimplication a+b (had ...

We propose and study a probabilistic logic over an algebraic basis, including equations and domain restrictions. The logic combines aspects from classical logic and equational logic with an exogenous approach to quantitative probabilistic reasoning. We present a sound and weakly complete axiomatization for the logic, parameterized by an equational specification of the algebraic basis coupled wi...

Algebraic logic compacts many small steps of general logical derivation into large steps of equational reasoning. We illustrate this by representing epistemic logic and game logic in modal semirings and modal Kleene algebras.

Equational problems (i.e.: rst-order formulae with quantiier preex 9 8 , whose only predicate symbol is syntactic equality) are an important tool in many areas of Computer Science like automated deduction, automated model building, logic programming , functional programming, etc. The aim of this work is a complexity analysis of the satissability problem of equational problems over a nite domain...

Action logic of Pratt [21] can be presented as Full Lambek Calculus FL [14, 17] enriched with Kleene star *; it is equivalent to the equational theory of residuated Kleene algebras (lattices). Some results on axiom systems, complexity and models of this logic were obtained in [4, 3, 18]. Here we prove a stronger form of *-elimination for the logic of *-continuous action lattices and the Π1−comp...

The definition of identity in terms of other logical symbols is a recurrent issue in logic. In particular, in First-Order Logic (FOL) there is no way of defining the global relation of identity, while in standard Second-Order Logic (SOL) this definition is not only possible, but widely used. In this paper, the reverse question is posed and affirmatively answered: Can we define with only equalit...