We represent properties of actions in a logic programming language that uses both classical negation and negation as failure. The method is applicable to temporal projection problems with incomplete information, as well as to reasoning about the past. It is proved to be sound relative to a semantics of action based on states and transition functions. 1 Introduction This paper extends the work of Eshghi and Kowalski [6], Evans [7] and Apt and Bezem [1] on representing properties of actions in logic programming languages with negation as failure. Our goal is to overcome some of the limitations of the earlier work. The existing formalizations of action in logic programming are adequate for only the simplest kind of temporal reasoning---"temporal projection." In a temporal projection problem, we are given a description of the initial state of the world, and use properties of actions to determine what the world will look like after a series of actions is performed. Moreover, the existing ...

We pursue the perspective of Reiter that in the situation calculus one can formalize primitive, determinate actions with axioms which, among others, include two disjoint sets: a set of successor state axioms and a set of action precondition axioms. We posed ourselves the problem of automatically generating successor state axioms, given only a set of effect axioms and a set of state constraints. This is a special version of what has been traditionally called the ramification problem. To our surprise, we found that there are state constraints whose role is not to yield indirect effects of actions. Rather, they are implicit axioms about action preconditions. As such, they are intimately related to the classical qualification problem. We also discovered that other kinds of state constraints arise; these are related to the formalization of strategic or control information. This paper is devoted to describing our results along these lines, focusing on ramification and qualification state con...

We define and study a high-level language for describing actions, more expressive than the action language A introduced by Gelfond and Lifschitz. The new language, AR, allows us to describe actions with indirect effects (ramifications), nondeterministic actions, and actions that may be impossible to execute. It has symbols for nonpropositional fluents and for the fluents that are exempt from the commonsense law of inertia. Temporal projection problems specified using the language AR can be represented as nested abnormality theories based on the situation calculus.

In presence of incomplete information about the world we need to distinguish between the state of the world and the state of the agent’s knowledge about the world. In such a case the agent may need to have at its disposal sensing actions that change its state of knowledge about the world and may need to construct more general plans consisting of sensing actions and conditional statements to achieve its goal. In this paper we first develop a high-level action description language that allows specification of sensing actions and their effects in its domain description and allows queries with conditional plans. We give provably correct translations of domain description in our language to axioms in first-order logic, and relate our formulation to several earlier formulations in the literature. We then analyze the state space of our formulation and develop several sound approximations that have much smaller state spaces. Finally we define regression of knowledge formulas over conditional plans,

We present the basic framework of a logic of actions and plans defined in terms of modal logic combined with a notion of dependence. The latter is used as a weak causal connection between actions and literals. In this paper we focus on the frame problem and demonstrate how it can be solved in our framework in a simple and monotonic way. We give the semantics, and associate an axiomatics and a decision procedure to it. The decision procedure is based on a sound and complete tableau method with single step rules to treat dependence. We show how it can be used to generate plans. Our solution is formally assessed by a translation of Gelfond and Lifschitz' logic A. We briefly sketch the second part of the paper, showing how we can go beyond A by some examples involving nondeterminism and ramifications.

this paper we extend the language A and its translation to allow reasoning about the effects of concurrent actions. The logic programming formalization of situation calculus with concurrent actions presented in the paper is of independent interest and may serve as a test bed for the investigation of various transformations and logic programming inference mechanisms. ! 1. INTRODUCTION

this paper, we present an equational logic framework for objects, methods, inheritance and overriding of methods. Overriding is achieved via the concept of specificity, which states that more specific methods are preferred to less specific ones. Specificity is computed with the help of negation as failure. We specify equational logic programs and show that their completed versions behave as intended. Furthermore, we prove that SLDENF-resolution is complete if the equational theory is finitary, the completed programs are consistent, and no derivation flounders or is infinite; and we give syntactic conditions which guarantee non-floundering and finiteness. Finally, we discuss how the approach can be extended to reasoning about the past in the context of incompletely specified objects or situations. It will turn out that constructive negation is needed to solve these problems

We propose a modification L 1 of the action description language A. The language L 1 allows representation of hypothetical situations and hypothetical occurrence of actions (as in A) as well as representation of actual occurrences of actions and observations of the truth values of fluents in actual situations. The corresponding entailment relation formalizes various types of common-sense reasoning about actions and their effects not modeled by previous approaches. As an application of L 1 we also present an architecture for intelligent agents capable of observing, planning and acting in a changing environment based on the entailment relation of L 1 and use logic programming approximation of this entailment to implement a planning module for this architecture. We prove the soundness of our implementation and give a sucient condition for its completeness.

Abstract. The Event Calculus is a narrative based formalism for reasoning about actions and change originally proposed in logic programming form by Kowalski and Sergot. In this paper we summarise how variants of the Event Calculus may be expressed as classical logic axiomatisations, and how under certain circumstances these theories may be reformulated as “action description language ” domain descriptions using the Language E. This enables the classical logic Event Calculus to inherit various provably correct automated reasoning procedures recently developed for E. 1

Andrew Baker's approach to reasoning about actions is the most robust circumscriptive approach currently known. Investigation of its applicability to nondeterministic actions reveals that this approach does not allow us to draw some intuitively plausible conclusions. Also, it does not always generate the proper existence of situations axiom. The limitations are traced to an unexpected interference of the axioms encoding observations with the minimization. A modification that avoids the shortcomings is suggested. 1 Introduction It has long been recognized [McCarthy and Hayes, 1969] that the frame problem, viz. the problem of formalizing in a natural and succinct fashion what is unchanged as a result of performing an action, is central to reasoning about change. This problem has been one of the motivating factors behind the emergence of several nonmonotonic formalisms [McCarthy, 1980; Reiter, 1980; McDermott and Doyle, 1980] in the 80's. McCarthy in his 1986 paper ([McCarthy, 1986]) p...