Simple improvements of a simple solution for inverting resolution

In this paper we address some simple improvements of the algorithm of Rouveirol and Puget [1989] for inverting resolution. Their approach is based on automatic change of representation called flattening and unflattening of clauses in a logic program. This enables a simple implementation of operators, such as Absorption, presented in Muggleton and Buntine [1988]. Unfortunately both the algorithms of MB and RP are incomplete. We analyze the reasons of the incompleteness of the RP algorithm and present an improved Absorption operator. It appears that flat tree epresentations of clauses and predicate calculus with equality provide an appropriate context for these matters

The logic of causal propositions

The first part of the paper_ outlines the development of causality in Greek philosophy. Some remarks are made on how some medieval philosophers approached to the problem. The paper shows also how modern philosophy understood causation. The paper inquires into the characteristics of causal relation as it is accepted in the domain of modern and recent physics.In the second part of the paper one finds some remarks concerning the programme of construing a new system CI of logic of causal propositions. This system is adequate to the manner in which causality is presented in physics. The system CI is being construed to characterize the connective of relativistic conditionals ‘$\rightsquigarrow$’ by means of the methods of recent logic. This connective should be read as follows: ‘if …, then for that reason …’. The arguments of the connective ‘$\rightsquigarrow$’ may be propositional formulas describing a particular event. The new system of non-classical logic is based on the classical propositional calculus, on the one of systems of temporal logic, and on a system ZI of logic of change. The findings concerning causation, as outlined in the first part of the paper, constitute descriptive semantics of the system CI presented in the second part of the paper. This system may play a positive role in the indirect justification of theorems in philosophy in a broad sense

Modal logics of sabotage revisited

Sabotage modal logic was proposed in 2003 as a format for analysing games that modify graphs they are played on. We investigate some model-theoretic and proof-theoretic aspects of sabotage modal logic, which has come to be viewed as an early dynamic logic of graph change. Our first result is a characterization theorem for sabotage modal logic as a fragment of first-order logic which is invariant with respect to a natural notion of ‘sabotage bisimulation’. Next, we offer a sound and complete tableau method and its associated labelled sequent calculus for analysing reasoning in sabotage modal logic. Finally, we identify and briefly explore a number of open research problems concerning sabotage modal logic that illuminate its complexity, placing it within the current landscape of modal logics that analyse model update, and, returning to the original motivation of sabotage, fixed-point logics for network games

A logic programming framework for modeling temporal objects

Published versio

Tool support for reasoning in display calculi

We present a tool for reasoning in and about propositional sequent calculi. One aim is to support reasoning in calculi that contain a hundred rules or more, so that even relatively small pen and paper derivations become tedious and error prone. As an example, we implement the display calculus D.EAK of dynamic epistemic logic. Second, we provide embeddings of the calculus in the theorem prover Isabelle for formalising proofs about D.EAK. As a case study we show that the solution of the muddy children puzzle is derivable for any number of muddy children. Third, there is a set of meta-tools, that allows us to adapt the tool for a wide variety of user defined calculi

Temporal Data Modeling and Reasoning for Information Systems

Temporal knowledge representation and reasoning is a major research field in Artificial Intelligence, in Database Systems, and in Web and Semantic Web research. The ability to model and process time and calendar data is essential for many applications like appointment scheduling, planning, Web services, temporal and active database systems, adaptive Web applications, and mobile computing applications. This article aims at three complementary goals. First, to provide with a general background in temporal data modeling and reasoning approaches. Second, to serve as an orientation guide for further specific reading. Third, to point to new application fields and research perspectives on temporal knowledge representation and reasoning in the Web and Semantic Web