A Logic of Knowing How

In this paper, we propose a single-agent modal logic framework for reasoning about goal-direct "knowing how" based on ideas from linguistics, philosophy, modal logic and automated planning. We first define a modal language to express "I know how to guarantee phi given psi" with a semantics not based on standard epistemic models but labelled transition systems that represent the agent's knowledge of his own abilities. A sound and complete proof system is given to capture the valid reasoning patterns about "knowing how" where the most important axiom suggests its compositional nature.Comment: 14 pages, a 12-page version accepted by LORI

Cut Elimination for a Logic with Induction and Co-induction

Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles are based on a proof theoretic (rather than set-theoretic) notion of definition. Definitions are akin to logic programs, where the left and right rules for defined atoms allow one to view theories as "closed" or defining fixed points. The use of definitions and free equality makes it possible to reason intentionally about syntax. We add in a consistent way rules for pre and post fixed points, thus allowing the user to reason inductively and co-inductively about properties of computational system making full use of higher-order abstract syntax. Consistency is guaranteed via cut-elimination, where we give the first, to our knowledge, cut-elimination procedure in the presence of general inductive and co-inductive definitions.Comment: 42 pages, submitted to the Journal of Applied Logi

PaL Diagrams: A Linear Diagram-Based Visual Language

Linear diagrams have recently been shown to be more effective than Euler diagrams when used for set-based reasoning. However, unlike the growing corpus of knowledge about formal aspects of Euler and Venn diagrams, there has been no formalisation of linear diagrams. To fill this knowledge gap, we present and formalise Point and Line (PaL) diagrams, an extension of simple linear diagrams containing points, thus providing a formal foundation for an effective visual language.We prove that PaL diagrams are exactly as expressive as monadic first-order logic with equality, gaining, as a corollary, an equivalence with the Euler diagram extension called spider diagrams. The method of proof provides translations between PaL diagrams and sentences of monadic first-order logic

Integrating Case-Based Reasoning with Adaptive Process Management

The need for more flexiblity of process-aware information systems (PAIS) has been discussed for several years and different approaches for adaptive process management have emerged. Only few of them provide support for both changes of individual process instances and the propagation of process type changes to a collection of related process instances. The knowledge about changes has not yet been exploited by any of these systems. To overcome this practical limitation, PAIS must capture the whole process life cycle and all kinds of changes in an integrated way. They must allow users to deviate from the predefined process in exceptional situations, and assist them in retrieving and reusing knowledge about previously performed changes. In this report we present a proof-of concept implementation of a learning adaptive PAIS. The prototype combines the ADEPT2 framework for dynamic process changes with concepts and methods provided by case-based reasoning(CBR) technology

On Distributive Subalgebras of Qualitative Spatial and Temporal Calculi

Qualitative calculi play a central role in representing and reasoning about qualitative spatial and temporal knowledge. This paper studies distributive subalgebras of qualitative calculi, which are subalgebras in which (weak) composition distributives over nonempty intersections. It has been proven for RCC5 and RCC8 that path consistent constraint network over a distributive subalgebra is always minimal and globally consistent (in the sense of strong $n$-consistency) in a qualitative sense. The well-known subclass of convex interval relations provides one such an example of distributive subalgebras. This paper first gives a characterisation of distributive subalgebras, which states that the intersection of a set of $n\geq 3$ relations in the subalgebra is nonempty if and only if the intersection of every two of these relations is nonempty. We further compute and generate all maximal distributive subalgebras for Point Algebra, Interval Algebra, RCC5 and RCC8, Cardinal Relation Algebra, and Rectangle Algebra. Lastly, we establish two nice properties which will play an important role in efficient reasoning with constraint networks involving a large number of variables.Comment: Adding proof of Theorem 2 to appendi