The complexity of theorem proving in circumscription and minimal entailment

We provide the first comprehensive proof-complexity analysis of different proof systems for propositional circumscription. In particular, we investigate two sequent-style calculi: MLK defined by Olivetti [28] and CIRC introduced by Bonatti and Olivetti [8], and the tableaux calculus NTAB suggested by Niemelä [26]. In our analysis we obtain exponential lower bounds for the proof size in NTAB and CIRC and show a polynomial simulation of CIRC by MLK. This yields a chain NTAB < CIRC < MLK of proof systems for circumscription of strictly increasing strength with respect to lengths of proofs

Super Logic Programs

The Autoepistemic Logic of Knowledge and Belief (AELB) is a powerful nonmonotic formalism introduced by Teodor Przymusinski in 1994. In this paper, we specialize it to a class of theories called `super logic programs'. We argue that these programs form a natural generalization of standard logic programs. In particular, they allow disjunctions and default negation of arbibrary positive objective formulas. Our main results are two new and powerful characterizations of the static semant ics of these programs, one syntactic, and one model-theoretic. The syntactic fixed point characterization is much simpler than the fixed point construction of the static semantics for arbitrary AELB theories. The model-theoretic characterization via Kripke models allows one to construct finite representations of the inherently infinite static expansions. Both characterizations can be used as the basis of algorithms for query answering under the static semantics. We describe a query-answering interpreter for super programs which we developed based on the model-theoretic characterization and which is available on the web.Comment: 47 pages, revised version of the paper submitted 10/200

A general approach to temporal reasoning about action and change

Reasoning about actions and change based on common sense knowledge is one of the most important and difficult tasks in the artificial intelligence research area. A series of such tasks are identified which motivate the consideration and application of reasoning formalisms. There follows a discussion of the broad issues involved in modelling time and constructing a logical language. In general, worlds change over time. To model the dynamic world, the ability to predict what the state of the world will be after the execution of a particular sequence of actions, which take time and to explain how some given state change came about, i.e. the causality are basic requirements of any autonomous rational agent. The research work presented herein addresses some of the fundamental concepts and the relative issues in formal reasoning about actions and change. In this thesis, we employ a new time structure, which helps to deal with the so-called intermingling problem and the dividing instant problem. Also, the issue of how to treat the relationship between a time duration and its relative time entity is examined. In addition, some key terms for representing and reasoning about actions and change, such as states, situations, actions and events are formulated. Furthermore, a new formalism for reasoning about change over time is presented. It allows more flexible temporal causal relationships than do other formalisms for reasoning about causal change, such as the situation calculus and the event calculus. It includes effects that start during, immediately after, or some time after their causes, and which end before, simultaneously with, or after their causes. The presented formalism allows the expression of common-sense causal laws at high level. Also, it is shown how these laws can be used to deduce state change over time at low level. Finally, we show that the approach provided here is expressive