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Theory blending: extended algorithmic aspects and examples
In Cognitive Science, conceptual blending has been proposed as an important cognitive mechanism that facilitates the creation of new concepts and ideas by constrained combination of available knowledge. It thereby provides a possible theoretical foundation for modeling high-level cognitive faculties such as the ability to understand, learn, and create new concepts and theories. Quite often the development of new mathematical theories and results is based on the combination of previously independent concepts, potentially even originating from distinct subareas of mathematics. Conceptual blending promises to offer a framework for modeling and re-creating this form of mathematical concept invention with computational means. This paper describes a logic-based framework which allows a formal treatment of theory blending (a subform of the general notion of conceptual blending with high relevance for applications in mathematics), discusses an interactive algorithm for blending within the framework, and provides several illustrating worked examples from mathematics
Stone-type representations and dualities for varieties of bisemilattices
In this article we will focus our attention on the variety of distributive
bisemilattices and some linguistic expansions thereof: bounded, De Morgan, and
involutive bisemilattices. After extending Balbes' representation theorem to
bounded, De Morgan, and involutive bisemilattices, we make use of Hartonas-Dunn
duality and introduce the categories of 2spaces and 2spaces. The
categories of 2spaces and 2spaces will play with respect to the
categories of distributive bisemilattices and De Morgan bisemilattices,
respectively, a role analogous to the category of Stone spaces with respect to
the category of Boolean algebras. Actually, the aim of this work is to show
that these categories are, in fact, dually equivalent
Graph Grammars for Knowledge Representation
This report consists of two papers presented at the March 1990 GRAGRA meeting in Bremen: the more general ''Representation of knowledge using graph grammars'' which argues for graphs as the universal KR formalism and the more specific ''The four musicians: analogies and expert systems -- a graphic approach'' which demonstrates the use of graphics for type inheritance and analogical reasoning
ASP, Amalgamation and the Conceptual Blending Workflow
We present a framework for conceptual blending – a concept invention method that is advocated in cognitive science as a fundamental, and uniquely human engine for creative thinking. Herein, we employ the search capabilities of ASP to find commonalities among input concepts as part of the blending process, and we show how our approach fits within a generalised conceptual blending workflow. Specifically, we orchestrate ASP with imperative Python programming, to query external tools for theorem proving and colimit computation. We exemplify our approach with an example of creativity in mathematics. © Springer International Publishing Switzerland 2015.This work is supported by the 7th Framework Programme for Research of the European Commission funded COINVENT project (FET-Open grant number: 611553). M. Eppe is supported by the German Academic Exchange ServicePeer Reviewe
Composition of hierarchic default specifications
[no abstract
Ologs: a categorical framework for knowledge representation
In this paper we introduce the olog, or ontology log, a category-theoretic
model for knowledge representation (KR). Grounded in formal mathematics, ologs
can be rigorously formulated and cross-compared in ways that other KR models
(such as semantic networks) cannot. An olog is similar to a relational database
schema; in fact an olog can serve as a data repository if desired. Unlike
database schemas, which are generally difficult to create or modify, ologs are
designed to be user-friendly enough that authoring or reconfiguring an olog is
a matter of course rather than a difficult chore. It is hoped that learning to
author ologs is much simpler than learning a database definition language,
despite their similarity. We describe ologs carefully and illustrate with many
examples. As an application we show that any primitive recursive function can
be described by an olog. We also show that ologs can be aligned or connected
together into a larger network using functors. The various methods of
information flow and institutions can then be used to integrate local and
global world-views. We finish by providing several different avenues for future
research.Comment: 38 page
Bounded Situation Calculus Action Theories
In this paper, we investigate bounded action theories in the situation
calculus. A bounded action theory is one which entails that, in every
situation, the number of object tuples in the extension of fluents is bounded
by a given constant, although such extensions are in general different across
the infinitely many situations. We argue that such theories are common in
applications, either because facts do not persist indefinitely or because the
agent eventually forgets some facts, as new ones are learnt. We discuss various
classes of bounded action theories. Then we show that verification of a
powerful first-order variant of the mu-calculus is decidable for such theories.
Notably, this variant supports a controlled form of quantification across
situations. We also show that through verification, we can actually check
whether an arbitrary action theory maintains boundedness.Comment: 51 page
A mathematical formulation of intelligent agents and their activities
Includes bibliography: leaves 119-126.The task of optimising a collection of objective functions subject to a set of constraints is as important to industry as it is ubiquitous. The importance of this task is evidenced by the amount of research on this subject that is currently in progress. Although this problem has been solved satisfactorily in a number of domains, new techniques and formalisms are still being devised that are applicable in fields as diverse as digital filter design and software engineering. These methods, however, are often computationally intensive, and the heavy reliance on numeric processing usually renders them unintuitive. A further limitation is that many of the techniques treat the problem in top-down fashion. This approach often manifests itself in large, complex systems of equations that are difficult to solve and adapt. By contrast, in a bottom-up approach, a given task is distributed over a collection of smaller components. These components embed behaviour that is determined by simple rules. The interactions between the components, however, often yield behaviour, the complexity of which surpasses what can be captured by the systems of equations that arise from a top-down approach. In this dissertation, we wish to study this bottom-up approach in more detail. Our aim is not to solve the optimisation problem, but rather, to study the smaller components of the approach and their behaviour more closely. To model the components, we choose intelligent agents because these represent a simple yet effective paradigm for capturing complex behaviour with simple rules. We provide several representations for the agents, each of which enables us to model a different aspect of their behaviour. To formulate the representations, we use techniques and concepts from fields such as universal algebra, order theory, domain theory and topology. As part of the formulation we also present a case study to demonstrate how the formulation could be applied
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