A Temporal extension of Prolog

AbstractTemporal Prolog, a temporal logic extension of PROLOG, is presented. The primary criterion for the model selection has been its natural embedment into the logic programming paradigm. Under strong efficiency constraints, a first-order “reified” logic has been taken as a basis for the implementation. Allen's temporal constraint algorithm has been extended for treatment of retractable constraints. Their embedment into Temporal Prolog can be viewed as an instance of the Constraint Logic Programming paradigm. An example inspired by K. Forbus's Qualitative Process Theory illustrates how qualitative simulation and related tasks can be formulated in Temporal Prolog in a transparent and declarative way

Subsumption in Modal Logic

Subsumption has long been known as a technique to detect redundant clauses in the search space of automated deduction systems for classical first order logic. In recent years several automated deduction methods for non-classical modal logics have been developed. This thesis explores, how subsumption can be made to work in the context of these modal logic deduction methods. Many modern modal logic deduction methods follow an indirect approach. They translate the modal sentences into some other target language, and then determine whether there exists a proof in that language, rather than doing deduction in the modal language itself. Consequently, subsumption then needs to focus on the target language, in which the actual proof is done. World Path Logic (WPL) is introduced as a possible target language. Deduction in WPL works very much like in ordinary logic, the only significant difference is the need for a special purpose unification, which unifies world paths under an equational theory (E-unification). Relating WPL to a well understood first order logic of restricted quantification, the properties of WPL, that make deduction work, are examined. The obtained theoretical results are the basis for the following treatment of subsumption in WPL. Subsumption is analyzed treating a clause as a scheme standing for the set of its ground instances. Although the notion of ground instances in WPL is different from ordinary logic, it turns out that - just like in ordinary logic - a clause Cl subsumes another clause C2, if there exists a substitution 6 such that C10 £ C2. Once the special purpose unification has been implemented into a theorem prover to allow for deduction in WPL, existing subsumption tests then work without any further changes

A cookbook for temporal conceptual data modelling with description logic

We design temporal description logics suitable for reasoning about temporal conceptual data models and investigate their computational complexity. Our formalisms are based on DL-Lite logics with three types of concept inclusions (ranging from atomic concept inclusions and disjointness to the full Booleans), as well as cardinality constraints and role inclusions. In the temporal dimension, they capture future and past temporal operators on concepts, flexible and rigid roles, the operators `always' and `some time' on roles, data assertions for particular moments of time and global concept inclusions. The logics are interpreted over the Cartesian products of object domains and the flow of time (Z,<), satisfying the constant domain assumption. We prove that the most expressive of our temporal description logics (which can capture lifespan cardinalities and either qualitative or quantitative evolution constraints) turn out to be undecidable. However, by omitting some of the temporal operators on concepts/roles or by restricting the form of concept inclusions we obtain logics whose complexity ranges between PSpace and NLogSpace. These positive results were obtained by reduction to various clausal fragments of propositional temporal logic, which opens a way to employ propositional or first-order temporal provers for reasoning about temporal data models

Automated Analysis of Compositional Multi-Agent Systems

Abstract. An approach for handling the complex dynamics of a multi-agent system is based on distinguishing aggregation levels. The behaviour at a given aggregation level is specified by a set of dynamic properties at that level, expressed in some (temporal) language. Such behavioural specifications may be complex and difficult to analyse. To enable automated analysis of system specifications, a simpler format is required. To this end, a specification at a lower aggregation level can be created, describing basic steps in the processes of a system. This paper presents a method and tool to support the automated creation of such a specification, as a refinement of a given higher level specification. The generated specification has a simple format which can easily be used for analysis. This paper describes an approach for automated verification of logical consequences of specifications using model checking techniques

Efficient Constraints on Possible Worlds for Reasoning about Necessity

Modal logics offer natural, declarative representations for describing both the modular structure of logical specifications and the attitudes and behaviors of agents. The results of this paper further the goal of building practical, efficient reasoning systems using modal logics. The key problem in modal deduction is reasoning about the world in a model (or scope in a proof) at which an inference rule is applied—a potentially hard problem. This paper investigates the use of partial-order mechanisms to maintain constraints on the application of modal rules in proof search in restricted languages. The main result is a simple, incremental polynomial-time algorithm to correctly order rules in proof trees for combinations of K, K4, T and S4 necessity operators governed by a variety of interactions, assuming an encoding of negation using a scoped constant ┴. This contrasts with previous equational unification methods, which have exponential performance in general because they simply guess among possible intercalations of modal operators. The new, fast algorithm is appropriate for use in a wide variety of applications of modal logic, from planning to logic programming

Pseudo-contractions as Gentle Repairs

Updating a knowledge base to remove an unwanted consequence is a challenging task. Some of the original sentences must be either deleted or weakened in such a way that the sentence to be removed is no longer entailed by the resulting set. On the other hand, it is desirable that the existing knowledge be preserved as much as possible, minimising the loss of information. Several approaches to this problem can be found in the literature. In particular, when the knowledge is represented by an ontology, two different families of frameworks have been developed in the literature in the past decades with numerous ideas in common but with little interaction between the communities: applications of AGM-like Belief Change and justification-based Ontology Repair. In this paper, we investigate the relationship between pseudo-contraction operations and gentle repairs. Both aim to avoid the complete deletion of sentences when replacing them with weaker versions is enough to prevent the entailment of the unwanted formula. We show the correspondence between concepts on both sides and investigate under which conditions they are equivalent. Furthermore, we propose a unified notation for the two approaches, which might contribute to the integration of the two areas

Representing scope in intuitionistic deductions

AbstractIntuitionistic proofs can be segmented into scopes which describe when assumptions can be used. In standard descriptions of intuitionistic logic, these scopes occupy contiguous regions of proofs. This leads to an explosion in the search space for automated deduction, because of the difficulty of planning to apply a rule inside a particular scoped region of the proof. This paper investigates an alternative representation which assigns scope explicitly to formulas, and which is inspired in part by semantics-based translation methods for modal deduction. This calculus is simple and is justified by direct proof-theoretic arguments that transform proofs in the calculus so that scopes match standard descriptions. A Herbrand theorem, established straightforwardly, lifts this calculus to incorporate unification. The resulting system has no impermutabilities whatsoever — rules of inference may be used equivalently anywhere in the proof. Nevertheless, a natural specification describes how λ-terms are to be extracted from its deductions

Representing Scope in Intuitionistic Deductions

Intuitionistic proofs can be segmented into scopes which describe when assumptions can be used. In standard descriptions of intuitionistic logic, these scopes occupy contiguous regions of proofs. This leads to an explosion in the search space for automated deduction, because of the difficulty of planning to apply a rule inside a particular scoped region of the proof. This paper investigates an alternative representation which assigns scope explicitly to formulas, and which is inspired in part by semantics-based translation methods for modal deduction. This calculus is simple and is justified by direct proof-theoretic arguments that transform proofs in the calculus so that scopes match standard descriptions. A Herbrand theorem, established straightforwardly, lifts this calculus to incorporate unification. The resulting system has no impermutabilities whatsoever—rules of inference may be used equivalently anywhere in the proof. Nevertheless, a natural specification describes how λ-terms are to be extracted from its deductions