KLMLean 1.0: a Theorem Prover for Logics of Default Reasoning

Lecture Notes in Computer Science, 1993

We present what we call Constructive Default Logic (CDL) -a default logic in which the fixedpoint definition of extensions is replaced by a constructive definition which yield so-called constructive extensions. Selection functions are used to represent explicitly the control of the reasoning process in this default logic. It is well-known that Reiter's original default logic lacks, in general, a default proof theory. We will show that CDL does have a default proof theory, and we will also show that this is related to the fact that CDL has the existence property for constructive extensions and that it also has the semi-monotonicity property. Furthermore, we will also show that, with respect to some counter-examples that were suggested by Lukaszewicz, constructive extensions yield more intuitive conclusions than Reiter's extensions. Hence, constructive default logic does not only have heuristic advantages over Reiter's default theory from a computational point of view, but it is also more adequate with respect to knowledge representation.

Lecture Notes in Computer Science, 2013

We describe PreDeLo 1.0, a theorem prover for preferential Description Logics (DLs). These are nonmonotonic extensions of standard DLs based on a typicality operator T, which enjoys a preferential semantics. PreDeLo 1.0 is a Prolog implementation of labelled tableaux calculi for such extensions, and it is able to deal with the preferential extension of the basic DL ALC as well as with the preferential extension of the lightweight DL DL-Litecore. The Prolog implementation is inspired by the "lean" methodology, whose basic idea is that each axiom or rule of the tableaux calculi is implemented by a Prolog clause of the program. Concerning ALC, PreDeLo 1.0 considers two extensions based, respectively, on Kraus, Lehmann and Magidor's preferential and rational entailment. In this paper, we also introduce a tableaux calculus for checking entailment in the rational extension of ALC.

We present tableau calculi for some logics of nonmonotonic reasoning, as defined by Kraus, Lehmann and Magidor. We give a tableau proof procedure for all KLM logics, namely preferential, loop-cumulative, cumulative and rational logics. Our calculi are obtained by introducing suitable modalities to interpret conditional assertions. We provide a decision procedure for the logics considered, and we study their complexity.

Computing Research Repository, 2006

We present tableau calculi for some logics of nonmonotonic reasoning, as defined by Kraus, Lehmann and Magidor. We give a tableau proof procedure for all KLM logics, namely preferential, loop-cumulative, cumulative and rational logics. Our calculi are obtained by introducing suitable modalities to interpret conditional assertions. We provide a decision procedure for the logics considered, and we study their complexity.

The need to make default assumptions is frequently encountered in reasoning'about incompletely specified worlds. Inferences sanctioned by default are best viewed as beliefs which may well be modified or rejected by subsequent observations. It is this property which leads to the non.monotonJcity of any logic of defaults. In this paper we propose a logic for default reasoning. We then specialize our treatment to a very large class of commonly occurring defaults. For this class we develop a complete proof theory and show how to interface it with a top down resolution theorem prover. Finally, we provide criteria under which the revision of derived beliefs must be effected.

1996

We apply logic program development technology to de ne abstract proof procedures, in the form of logic programs, for computing the admissibility semantics for default reasoning proposed in 2]. The proof procedures are derived from a formal speci cation. The derivation guarantees the soundness of the proof procedures. The completeness of the proof procedures is shown by employing a technique of symbolic execution of logic programs to compute (an instance of) a relation implied by the speci cation.

Journal of Applied Non-Classical Logics, 2008

In this paper we focus on theorem proving for conditional logics. First, we give a detailed description of CondLean, a theorem prover for some standard conditional logics. CondLean is a SICStus Prolog implementation of some labeled sequent calculi for conditional logics recently introduced. It is inspired to the so called "lean" methodology, even if it does not fit this style in a rigorous manner. CondLean also comprises a graphical interface written in Java. Furthermore, we introduce a goal-directed proof search mechanism, derived from the above mentioned sequent calculi based on the notion of uniform proofs. Finally, we describe GOALDUCK, a simple SICStus Prolog implementation of the goal-directed calculus mentioned here above. Both the programs CondLean and GOALDUCK, together with their source code, are available for free download at .

Computational Intelligence, 1994

Default logic has been introduced for handling reasoning with incomplete knowledge. It has been widely studied, and various definitions have been proposed for it. Most of the variants have been defined by means of fixed points of some operator. We propose here another approach, which is based on a study of the way in which general rules with exceptions, used in a default reasoning process, can contradict one another. We then isolate sets of noncontradicting rules, as large as possible in order to exploit as much information as possible, and construct, for each of these sets of rules, the set of conclusions that can be deduced from it. We show that our framework encompasses most of the existing variants of default logic, allowing those variants to be compared from a knowledge representation point of view. Our approach also enables us to provide an operational definition of extensions in some interesting cases. Proof-theoretical and semantical aspects are investigated.

In this paper we present CondLean 3.1, a theorem prover for some standard conditional logics, namely CK, CK+ID, CK+MP, CK+CS, CK+CEM, and some of their combinations. CondLean 3.1 implements some sequent calculi for these logics, called SeqS, recently introduced. CondLean 3.1 also comprises a graphical user interface written in Java.

This paper describes an improvement on the analytic tableau method which simulates SL-resolution. It is implemented by a short and elegant Prolog program which is relatively efficient.