Author:

Abstract:

Constructive processes play an important role in knowledge representation. Indeed, there are many formal languages whose semantics can be characterized using fixpoint criteria, that simulate, for instance, human thought processes or mathematical construction principles. Such processes can be studied in an abstract, algebraic way. This allows common properties of such languages to be examined in general, without committing to any particular syntax or semantics. In a first part of this thesis, we examine two topics in this way: first, we look at modularity of theories and, second, we consider certain transformations that extend the vocabulary of a theory to simplify some of its formulas. In both cases, we find that single algebraic theorem about constructive processes suffices to derive (partial) generalizations of a number of different existing results for logic programs, autoepistemic logic, and default logic. In a second part of the thesis we examine the link between constructive processes and the concept of causality. We observe that causality has an inherent dynamic aspect, i.e., that, in essence, causal information concerns the evolution of a domain over time. Motivated by this observation, we construct a new representation language for causal knowledge, whose semantics is defined explicitly in terms of constructive processes. This is done in a probabilistic context, where the basic steps that make up the process are allowed to have non-deterministic effects. We then show that a theory in this language defines a unique probability distribution over the possible outcomes of such a process. This result offers an appealing explanation for the usefulness of causal information and links our explicitly dynamic approach to more static causal probabilistic modelling languages, such as Bayesian networks. We also show that this language, which we have constructed to be a natural formalization of a certain kind of causal statements, is closely related to logic programming. This result demonstrates that, under an appropriate formal semantics, a rule of a normal, a disjunctive or a certain kind of probabilistic logic program can be interpreted as a description of a causal event.