Clare Dixon

Clausal temporal resolution

In this article, we examine how clausal resolution can be applied to a specific, but widely used, nonclassical logic, namely discrete linear temporal logic. Thus, we first define a normal form for temporal formulae and show how arbitrary temporal formulae can be translated into the normal form, while preserving satisfiability. We then introduce novel resolution rules that can be applied to formulae in this normal form, provide a range of examples, and examine the correctness and complexity of this approach. Finally, we describe related work and future developments concerning this work.

A New Parenting-Based Group Intervention for Young Anxious Children: Results of a Randomized Controlled Trial

OBJECTIVE Despite recent advances, there are still no interventions that have been developed for the specific treatment of young children who have anxiety disorders. This study examined the impact of a new, cognitive-behaviorally based parenting intervention on anxiety symptoms. METHOD Families of 74 anxious children (aged 9 years or less) took part in a randomized controlled trial, which compared the new 10-session, group-format intervention with a wait-list control condition. Outcome measures included blinded diagnostic interview and self-reports from parents and children. RESULTS Intention-to-treat analyses indicated that children whose parent(s) received the intervention were significantly less anxious at the end of the study than those in the control condition. Specifically, 57% of those receiving the new intervention were free of their primary disorder, compared with 15% in the control condition. Moreover, 32% of treated children were free of any anxiety diagnosis at the end of the treatment period, compared with 6% of those in the control group. Treatment gains were maintained at 12-month follow-up. CONCLUSIONS This new parenting-based intervention may represent an advance in the treatment of this previously neglected group.

Resolution for Temporal Logics of Knowledge

A resolution based proof system for a temporal logic of knowledge is p re ented and shown to be correct. Such logics are useful for proving properties of distribut ed and multi-agent systems. Examples are given to illustrate the proof system. An extension of th e basic system to the multimodal case is given and illustrated using the ‘muddy children problem’.

On Formal Specification of Emergent Behaviours in Swarm Robotic Systems

It is a characteristic of swarm robotics that specifying overall emergent swarm behaviours in terms of the low-level behaviours of individual robots is very difficult. Yet if swarm robotics is to make the transition from the laboratory to real-world engineering realisation we need such specifications. This paper explores the use of temporal logic to formally specify, and possibly also prove, the emergent behaviours of a robotic swarm. The paper makes use of a simplified wireless connected swarm as a case study with which to illustrate the approach. Such a formal approach could be an important step toward a disciplined design methodology for swarm robotics.

Combinations of Modal Logics

There is increasing use of combinations of modal logics in bothfoundational and applied research areas. This article provides anintroduction to both the principles of such combinations and to thevariety of techniques that have been developed for them. In addition,the article outlines many key research problems yet to be tackledwithin this callenging area of work.

A Tableau-Based Proof Method for Temporal Logics of Knowledge and Belief

ABSTRACT In this paper we define two logics, KLn and BLn, and present tableau-based decision procedures for both. KLn is a temporal logic of knowledge. Thus, in addition to the usual connectives of linear discrete temporal logic, it contains a set of unary modal connectives for representing the knowledge possessed by agents. The logic BLn is somewhat similar; it is a temporal logic that contains connectives for representing the beliefs of agents. In addition to a complete formal definition of the two logics and their decision procedures, the paper includes a brief review of their applications in AI and mainstream computer science, correctness proofs for the decision procedures, a number of worked examples illustrating the decision procedures, and some pointers to further work.

Temporal resolution using a breadth-first search

An approach to applying clausal resolution, a proof method well suited to mechanisation, to temporal logics has been developed by Fisher. The method involves translation to a normal form, classical style resolution within states, and temporal resolution between states. Not only has it been shown to be correct but as it consists of only one temporal resolution rule, it is particularly suitable as the basis of an automated temporal resolution theorem prover. As the application of the temporal resolution rule is the most costly part of the method, it is on this area that we focus. Detailed algorithms for abreadth‐first search approach to the application of this rule are presented. Correctness is shown and complexity given. Analysis of the behaviour of the algorithms is carried out and we explain why this approach is an improvement to others suggested.

Using temporal logics of knowledge in the formal verification of security protocols

Temporal logics of knowledge are useful for reasoning about situations where the knowledge of an agent or component is important, and where change in this knowledge may occur over time. Here we use temporal logics of knowledge to reason about security protocols. We show how to specify part of the Needham-Schroeder protocol using temporal logics of knowledge and prove various properties using a clausal resolution calculus for this logic.

Search Strategies for Resolution in Temporal Logics

In this paper we give and evaluate the algorithms for a fully automated temporal resolution theorem prover. An approach to applying resolution, a proof method for classical logics suited to mechanisation, to temporal logics has been developed by Fisher. As the application of the temporal resolution rule is the most costly part of the method, involving search amongst graphs, we propose different algorithms on which to base an implementation. The paper concludes with a comparison of their performance.

A Resolution-Based Proof Method for Temporal Logics of Knowledge and Belief

In this paper we define two logics, KLn and BLn, and present resolution-based proof methods for both. KLn is a temporal logic of knowledge. Thus, in addition to the usual connectives of linear discrete temporal logic, it contains a set of unary modal connectives for representing the knowledge possessed by agents. The logic BLn is somewhat similar: it is a temporal logic that contains connectives for representing the beliefs of agents. The proof methods we present for these logics involve two key steps. First, a formula to be tested for unsatisfiability is translated into a normal form. Secondly, a family of resolution rules are used, to deal with the interactions between the various operators of the logics. In addition to a description of the normal form and the proof methods, we present some short worked examples and proposals for future work.