Order-Sorted Equational Computation

The expressive power of many-sorted equational logic can be greatly enhanced by allowing for subsorts and multiple function declarations. In this paper we study some computational aspects of such a logic. We start with a self-contained introduction to order-sorted equational logic including initial algebra semantics and deduction rules. We then present a theory of order-sorted term rewriting and show that the key results for unsorted rewriting extend to sort decreasing rewriting. We continue with a review of order-sorted unification and prove the basic results. In the second part of the paper we study hierarchical order-sorted specifications with strict partial functions. We define the appropriate homomorphisms for strict algebras and show that every strict algebra is base isomorphic to a strict algebra with at most one error element. For strict specifications, we show that their categories of strict algebras have initial objects. We validate our approach to partial functions by proving that completely defined total functions can be defined as partial without changing the initial algebra semantics. Finally, we provide decidable sufficient criteria for the consistency and strictness of ground confluent rewriting systems

COLAB : a hybrid knowledge representation and compilation laboratory

Knowledge bases for real-world domains such as mechanical engineering require expressive and efficient representation and processing tools. We pursue a declarative-compilative approach to knowledge engineering. While Horn logic (as implemented in PROLOG) is well-suited for representing relational clauses, other kinds of declarative knowledge call for hybrid extensions: functional dependencies and higher-order knowledge should be modeled directly. Forward (bottom-up) reasoning should be integrated with backward (top-down) reasoning. Constraint propagation should be used wherever possible instead of search-intensive resolution. Taxonomic knowledge should be classified into an intuitive subsumption hierarchy. Our LISP-based tools provide direct translators of these declarative representations into abstract machines such as an extended Warren Abstract Machine (WAM) and specialized inference engines that are interfaced to each other. More importantly, we provide source-to-source transformers between various knowledge types, both for user convenience and machine efficiency. These formalisms with their translators and transformers have been developed as part of COLAB, a compilation laboratory for studying what we call, respectively, "vertical\u27; and "horizontal\u27; compilation of knowledge, as well as for exploring the synergetic collaboration of the knowledge representation formalisms. A case study in the realm of mechanical engineering has been an important driving force behind the development of COLAB. It will be used as the source of examples throughout the paper when discussing the enhanced formalisms, the hybrid representation architecture, and the compilers

An integration framework for managing rich organisational process knowledge

The problem we have addressed in this dissertation is that of designing a pragmatic framework for integrating the synthesis and management of organisational process knowledge which is based on domain-independent AI planning and plan representations. Our solution has focused on a set of framework components which provide methods, tools and representations to accomplish this task.In the framework we address a lifecycle of this knowledge which begins with a methodological approach to acquiring information about the process domain. We show that this initial domain specification can be translated into a common constraint-based model of activity (based on the work of Tate, 1996c and 1996d) which can then be operationalised for use in an AI planner. This model of activity is ontologically underpinned and may be expressed with a flexible and extensible language based on a sorted first-order logic. The model combines perspectives covering both the space of behaviour as well as the space of decisions. Synthesised or modified processes/plans can be translated to and from the common representation in order to support knowledge sharing, visualisation and mixed-initiative interaction.This work united past and present Edinburgh research on planning and infused it with perspectives from design rationale, requirements engineering, and process knowledge sharing. The implementation has been applied to a portfolio of scenarios which include process examples from business, manufacturing, construction and military operations. An archive of this work is available at: http://www.aiai.ed.ac.uk/~oplan/cpf