Autoepistemic Logic Research Articles

Logics for reasoning about knowledge and belief

AbstractAI researchers are becoming increasingly aware of the importance of reasoning about knowledge and belief. This paper reviews epistemic logic, a logic designed specifically for this type of reasoning. I introduce epistemic logic, and discuss some of the philosophical problems associated with it. I then compare two different styles of implementing theorem provers for epistemic logic. I also briefly discuss autoepistemic logic, a form of epistemic logic intended to model an agent's introspective reasoning, i.e. an agent's reasoning about its own beliefs. Finally, I discuss some of the proposals in the AI literature that are aimed at avoiding some of the philosophical problems that dog both epistemic and autoepistemic logic. This paper is not a full introduction to the field. Rather, it is intended to give the reader some flavour of the problems that research in this area faces, as well as some of the proposals for solving these problems.

On the declarative and procedural semantics of logic programs

One of the most important and difficult problems in logic programming is the problem of finding a suitable declarative or intended semantics for logic programs. The importance of this problem stems from the declarative character of logic programming, whereas its difficulty can be largely attributed to the non-monotonic character of the negation operator used in logic programs. The problem can therefore be viewed as the problem of finding a suitable formalization of the type of non-monotonic reasoning used in logic programming. In this paper we introduce a semantics of logic programs based on the class PERF(P) of all, not necessarily Herbrand, perfect models of a program P and we show that the proposed semantics is not only natural but it also combines many of the desirable features of previous approaches, at the same time eliminating some of their drawbacks. For a positive program P, the class PERF(P) of perfect models coincides with the class MIN(P) of all minimal models of P. The perfect model semantics is shown to be equivalent to the semantics of McCarthy's circumscription and is also equivalent to the remaining three major formalizations of non-monotonic reasoning in artificial intelligence-Reiter's closed world assumption, Moore's autoepistemic logic and Reiter's default theorythus establishing a closer link between the areas of logic programming and non-monotonic reasoning. We also define a generalization of SLD-resolution, called SLS-resolution and we prove that SLS-resolution is sound and complete with respect to the perfect model semantics.

Stable Theories in Autoepistemic Logic

We investigate the operator producing a stable theory out of its objective part (A stable theory is a set of beliefs of a rational agent). We characterize the objective parts of stable theories. Finally, we discuss the predicate calculus case.

Representing defaults with epistemic concepts

Reasoning about defaults—implications that typically hold, but which may have exceptions—is an important part of commonsense reasoning. We present some parts of a theory of defaults, concentrating on distinctions between various subtle ways in which defaults can be defeated, and on inferences which seem plausible but which are not correct in all cases. To represent this theory in a formal system, it is natural to use the epistemic concept of self‐belief. We show how to express the theory by a local translation into autoepistemic logic, which contains the requisite epistemic operators.

Nonmonotonic Logics – A Brief Overview

In this paper we describe the most important approaches to formalize nonmonotonic reasoning, in particular default reasoning: autoepistemic logic, default logic, circumscription, Delgrandes's conditional approach, and an approach based on preferred subtheories of the premises. Also the problem of mechanising these formalizations is discussed and some solutions developed so far are described.

On the relation between default and autoepistemic logic

Default logic is a formal means of reasoning about defaults: what normally is the case, in the absence of contradicting information. Autoepistemic logic, on the other hand, is meant to describe the consequences of reasoning about ignorance: what must be true if a certain fact is not known. Although the motivation and formal character of these two systems are different, a closer analysis shows that they share a common trait, which is the indexical nature of certain elements in the theory. In this paper we compare the expressive power of the two systems. First, we give an effective translation of default logic into autoepistemic logic; default theories can thus be embedded into autoepistemic logic. We also present a more surprising result: the reverse translation is also possible, so that every set of sentences in autoepistemic logic can be effectively rewritten as a default theory. The formal equivalence of these two differing systems is thus established. This analysis gives an interpretive semantics to default logic, and yields insight into the nature of defaults in autoepistemic reasoning.

Semantical considerations on nonmonotonic logic

Commonsense reasoning is ‘nonmonotonic’ in the sense that we often draw, on the basis of partial information, conclusions that we later retract when we are given more complete information. Some of the most interesting products of recent attempts to formalize nonmonotonic reasoning are the nonmonotonic logics of McDermott and Doyle [1, 2]. These logics, however, all have peculiarities that suggest they do not quite succeed in capturing the intuitions that prompted their development. In this paper we reconstruct nonmonotonic logic as a model of an ideally rational agent's reasoning about his own beliefs. For the resulting system, called autoepistemic logic, we define an intuitively based semantics for which we can show autoepistemic logic to be both sound and complete. We then compare autoepistemic logic with the approach of McDermott and Doyle, showing how it avoids the peculiarities of their nonmonotonic logic.