Approximations of modal logics: K and beyond

Inspired by the recent work on approximations of classical logic, we present a method that approximates several modal logics in a modular way. Our starting point is the limitation of the n-degree of introspection that is allowed, thus generating modal n-logics. The semantics for n-logics is presented, in which formulas are evaluated with respect to paths, and not possible worlds. A tableau-based proof system is presented, n-SST, and soundness and completeness is shown for the approximation of modal logics K, T, D, S4 and S5. (c) 2008 Published by Elsevier B.V.

Analytic Methods for the Logic of Proofs

The logic of proofs (lp) was proposed as Gdels missed link between Intuitionistic and S4-proofs, but so far the tableau-based methods proposed for lp have not explored this closeness with S4 and contain rules whose analycity is not immediately evident. We study possible formulations of analytic tableau proof methods for lp that preserve the subformula property. Two sound and complete tableau decision methods of increasing degree of analycity are proposed, KELP and preKELP. The latter is particularly inspired on S4-proofs. The crucial role of proof constants in the structure of lp-proofs methods is analysed. In particular, a method for the abduction of proof constant specifications in strongly analytic preKELP proofs is presented; abduction heuristics and the complexity of the method are discussed.

A logic-based agent that plans for extended reachability goals

Planning to reach a goal is an essential capability for rational agents. In general, a goal specifies a condition to be achieved at the end of the plan execution. In this article, we introduce nondeterministic planning for extended reachability goals (i.e., goals that also specify a condition to be preserved during the plan execution). We show that, when this kind of goal is considered, the temporal logic CTL turns out to be inadequate to formalize plan synthesis and plan validation algorithms. This is mainly due to the fact that the CTL`s semantics cannot discern among the various actions that produce state transitions. To overcome this limitation, we propose a new temporal logic called alpha-CTL. Then, based on this new logic, we implement a planner capable of synthesizing reliable plans for extended reachability goals, as a side effect of model checking.

New Improvements in Automatic Structure Elucidation Using the LSD (Logic for Structure Determination) and the SISTEMAT Expert Systems

This article describes the integration of the LSD (Logic for Structure Determination) and SISTEMAT expert systems that were both designed for the computer-assisted structure elucidation of small organic molecules. A first step has been achieved towards the linking of the SISTEMAT database with the LSD structure generator. The skeletal descriptions found by the SISTEMAT programs are now easily transferred to LSD as substructural constraints. Examples of the synergy between these expert systems are given for recently reported natural products.