A different perspective on canonicity

One of the most interesting aspects of Conceptual Structures Theory is the notion of canonicity. It is also one of the most neglected: Sowa seems to have abandoned it in the new version of the theory, and most of what has been written on canonicity focuses on the generalization hierarchy of conceptual graphs induced by the canonical formation rules. Although there is a common intuition that a graph is canonical if it is "meaningful'', the original theory is somewhat unclear about what that actually means, in particular how canonicity is related to logic. This paper argues that canonicity should be kept a first-class notion of Conceptual Structures Theory, provides a detailed analysis of work done so far, and proposes new definitions of the conformity relation and the canonical formation rules that allow a clear separation between canonicity and truth

Concept logics

Concept languages (as used in BACK, KL-ONE, KRYPTON, LOOM) are employed as knowledge representation formalisms in Artificial Intelligence. Their main purpose is to represent the generic concepts and the taxonomical hierarchies of the domain to be modeled. This paper addresses the combination of the fast taxonomical reasoning algorithms (e.g. subsumption, the classifier etc.) that come with these languages and reasoning in first order predicate logic. The interface between these two different modes of reasoning is accomplished by a new rule of inference, called constrained resolution. Correctness, completeness as well as the decidability of the constraints (in a restricted constraint language) are shown

Unification in sort theories and its applications

In this article I investigate the properties of unification in sort theories. The usual notion of a sort consisting of a sort symbol is extended to a set of sort symbols. In this language sorted unification in elementary sort theories is of unification type finitary. The rules of standard unification with the addition of four sorted rules form the new sorted unification algorithm. The algorithm is proved sound and complete. The rule based form of the algorithm is not suitable for an implementation because there is no control and the used data structures are weak. Therefore we transform the algorithm into a deterministic sorted unification procedure. For the procedure sorted unification in pseudo-linear sort theories is proved decidable. The notions of a sort and a sort theory are developed in a way such that a standard calculus can be turned into a sorted calculus by replacing standard unification with sorted unification. To this end sorts may denote the empty set. Sort theories may contain clauses with more than one declaration and may change dynamically during the deduction process. The applicability of the approach is exemplified for the resolution and the tableau calculus

Type theoretic semantics for semantic networks: an application to natural language engineering

Semantic Networks have long been recognised as an important tool for natural language processing. This research has been a formal analysis of a semantic network using constructive type theory. The particular net studied is SemNet, the internal knowledge representation for LOLITA(^1): a large scale natural language engineering system. SemNet has been designed with large scale, efficiency, integration and expressiveness in mind. It supports many different forms of plausible and valid reasoning, including: epistemic reasoning, causal reasoning and inheritance. The unified theory of types (UTT) integrates two well known type theories, Coquand-Huet's (impredicative) calculus of constructions and Martin-Lof's (predicative) type theory. The result is a strong and expressive language which has been used for formalization of mathematics, program specification and natural language. Motivated by the computational and richly expressive nature of UTT, this research has used it for formalization and semantic analysis of SemNet. Moreover, because of applications to software engineering, type checkers/proof assistants have been built. These tools are ideal for organising and managing the analysis of SemNet. The contribution of the work is twofold. First the semantic model built has led to improved and deeper understanding of SemNet. This is important as many researchers that work on different aspects of LOLITA, now have a clear and un- ambigious interpertation of the meaning of SemNet constructs. The model has also been used to show soundess of the valid reasoning and to give a reasonable semantic account of epistemic reasoning. Secondly the research contributes to NLE generally, both because it demonstrates that UTT is a useful formalization tool and that the good aspects of SemNet have been formally presented

Neuere Entwicklungen der deklarativen KI-Programmierung : proceedings

The field of declarative AI programming is briefly characterized. Its recent developments in Germany are reflected by a workshop as part of the scientific congress KI-93 at the Berlin Humboldt University. Three tutorials introduce to the state of the art in deductive databases, the programming language Gödel, and the evolution of knowledge bases. Eleven contributed papers treat knowledge revision/program transformation, types, constraints, and type-constraint combinations

Verification of Graph Programs

This thesis is concerned with verifying the correctness of programs written in GP 2 (for Graph Programs), an experimental, nondeterministic graph manipulation language, in which program states are graphs, and computational steps are applications of graph transformation rules. GP 2 allows for visual programming at a high level of abstraction, with the programmer freed from manipulating low-level data structures and instead solving graph-based problems in a direct, declarative, and rule-based way. To verify that a graph program meets some specification, however, has been -- prior to the work described in this thesis -- an ad hoc task, detracting from the appeal of using GP 2 to reason about graph algorithms, high-level system specifications, pointer structures, and the many other practical problems in software engineering and programming languages that can be modelled as graph problems. This thesis describes some contributions towards the challenge of verifying graph programs, in particular, Hoare logics with which correctness specifications can be proven in a syntax-directed and compositional manner. We contribute calculi of proof rules for GP 2 that allow for rigorous reasoning about both partial correctness and termination of graph programs. These are given in an extensional style, i.e. independent of fixed assertion languages. This approach allows for the re-use of proof rules with different assertion languages for graphs, and moreover, allows for properties of the calculi to be inherited: soundness, completeness for termination, and relative completeness (for sufficiently expressive assertion languages). We propose E-conditions as a graphical, intuitive assertion language for expressing properties of graphs -- both about their structure and labelling -- generalising the nested conditions of Habel, Pennemann, and Rensink. We instantiate our calculi with this language, explore the relationship between the decidability of the model checking problem and the existence of effective constructions for the extensional assertions, and fix a subclass of graph programs for which we have both. The calculi are then demonstrated by verifying a number of data- and structure-manipulating programs. We explore the relationship between E-conditions and classical logic, defining translations between the former and a many-sorted predicate logic over graphs; the logic being a potential front end to an implementation of our work in a proof assistant. Finally, we speculate on several avenues of interesting future work; in particular, a possible extension of E-conditions with transitive closure, for proving specifications involving properties about arbitrary-length paths

Teoria Básica das Estruturas Conceptuais

As Estruturas Conceptuais são um formalismo de representação de conhecimentos baseado em grafos, os chamados grafos conceptuais. A teoria foi inicialmente desenvolvida por John Sowa há dez anos. Desde então, uma comunidade científica cada vez mais ampla tem-na utilizado em muitas áreas de aplicação e propôs várias alterações à teoria original. Também está em desenvolvimento uma implementação estado-da-arte gratuita e, além disso, os grafos conceptuais foram adoptados num padrão ANSI em preparação. Apesar desta actividade não existe de facto uma definição formal, completa, consistente e revista da Teoria das Estruturas Conceptuais. Esta dissertação vem contribuir para essa definição ao estender, refinar e clarificar as noções básicas da teoria. A classificação dos grafos conceptuais em grafos sintacticamente correctos, grafos bem tipados, grafos ontologicamente correctos, chamados grafos canónicos, e grafos verdadeiros é a base da clarificação do significado das várias noções e serve de guia às extensões e aos refinamentos introduzidos. As principais extensões foram feitas no sistema de tipos e no esquema de dependências entre vértices de grafos, e o refinamento de quase todos os aspectos da teoria - em particular das regras de formação de grafos canónicos e das regras de inferência para os grafos verdadeiros - inclui o tratamento formal de algumas propostas informais de outros autores. [Conceptual Structures is a knowledge representation formalism based on graphs, the so called conceptual graphs. The theory was initially developed by John Sowa 10 years ago. Since then, it has been used by a growing scientific community in many application areas, and several changes to the original theory have been proposed. Furthermore, a freely available state-of-the-art implementation is under way and conceptual graphs were adopted by an ANSI standard currently in preparation. However, there still doesn't exist a complete, consistent and revised formal definition of Conceptual Structures Theory. This thesis extends, refines and clarifies the basic notions of the theory, thus contributing to its redefinition. The classification of conceptual graphs into syntactically correct graphs, well-typed graphs, ontologically correct graphs, called canonical graphs, and true graphs is the basis for the clarification of the notions' meaning, and it is the guideline for introducing extensions and making refinements. The main extensions proposed regard the type system and the dependencies among graph nodes. The refinements cover almost every aspect of the theory – particularly the formation rules for canonical graphs and the inference rules for true graphs – and include the formal treatment of some informal proposals done by other authors.