Heuristic-Driven Theory Projection: An Overview

Schmidt, Martin; Krumnack, Ulf; Gust, Helmar; Kühnberger, Kai‐Uwe

doi:10.1007/978-3-642-54516-0_7

Cited by 17 publications

(14 citation statements)

References 18 publications

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“…In our examples the inconsistencies will be discovered quickly 10 , but in more elaborate situations, a resourcebounded check for inconsistency may model reasonably well the experience of mathematicians who can work productively with theories that are believed to be consistent and later revise their results in case an inconsistency is found. Research on Nelson Oppen methods (see [7] for a survey) reveals conditions under which the satisfiability and decidability of two theories is preserved when taking their union.…”

Section: Theory Blending Algorithmmentioning

confidence: 54%

“…Our approach is based on the Heuristic-Driven Theory Projection (HDTP, [10]), a framework for computing analogical relations between two input spaces presented as axiomatizations in some many-sorted first-order languages. HDTP proceeds in two phases: in the mapping phase, the source and target spaces are compared to find structural commonalities and a generalized space G is created, which subsumes the matching parts of both spaces.…”

Section: Introductionmentioning

confidence: 99%

“…An anti-unifier of A and B is an expression E such that A and B can be obtained from E via substitutions. E is a least-general anti-unifier of A and B if it is an anti-unifier and the only susbtitutions on E that yield anti-unifiers of A and B act as trivial renamings of the variables in E. As it happens, first-order anti-unification (where only first-order substitutions are allowed) is not powerful enough to produce the generalizations needed in HDTP, so a special form of higher-order anti-unification is used where, under certain conditions, symbols of relation and function can also be included in the domain of substitutions (see [10] for the details). The generalized theory G can be projected into the original spaces by higher-order substitutions which are computed by HDTP during anti-unification.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Algorithmic Aspects of Theory Blending

Martinez

Krumnack

Smaill

et al. 2014

Artificial Intelligence and Symbolic Computation

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Abstract. 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. This paper describes a logic-based framework which allows a formal treatment of theory blending, discusses algorithmic aspects of blending within the framework, and provides an illustrating worked out example from mathematics.

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Section: Theory Blending Algorithmmentioning

confidence: 54%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Algorithmic Aspects of Theory Blending

Martinez

Krumnack

Smaill

et al. 2014

Artificial Intelligence and Symbolic Computation

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show abstract

“…In analogy engines, or (formal) approaches to conceptual blending (Turner, 2014;Kutz et al, 2014a), the presented graph of image schemas can provide a method for theory weakening and strengthening based on the involved image schemas, employing basic ideas of amalgams (Ontañón and Plaza, 2010). This approach is therefore substantially different from the more syntactic-driven methods used by the Structure Mapping Engine (SME) (Gentner, 1983;Forbus, Falkenhainer, and Gentner, 1989) or Heuristic-Driven Theory Projection (HDTP) (Schwering et al, 2009;Schmidt et al, 2014).…”

Section: Resultsmentioning

confidence: 99%

“…structure mapping (Gentner, 1983;Forbus, Falkenhainer, and Gentner, 1989) and heuristic-driven theory projection (HDPT) (Schmidt et al, 2014)) is the generation of a 'sensible' blend. In a completely automatised system, there is currently no simple way to distinguish the blendoids that a human would consider meaningful from those that lack cognitive value.…”

Section: Using Image Schemas In Computational Blendingmentioning

confidence: 99%

Choosing the Right Path: Image Schema Theory as a Foundation for Concept Invention

Hedblom

Kutz

Neuhaus

2015

Journal of Artificial General Intelligence

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Image schemas are recognised as a fundamental ingredient in human cognition and creative thought. They have been studied extensively in areas such as cognitive linguistics. With the goal of exploring their potential role in computational creative systems, we here study the viability of the idea to formalise image schemas as a set of interlinked theories. We discuss in particular a selection of image schemas related to the notion of 'path', and show how they can be mapped to a formalised family of microtheories reflecting the different aspects of path following. Finally, we illustrate the potential of this approach in the area of concept invention, namely by providing several examples illustrating in detail in what way formalised image schema families support the computational modelling of conceptual blending.

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Constructive Solving of Raven's IQ Tests with Analogical Proportions

Beltran

Prade

Richard

2016

Int. J. Intell. Syst.

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The paper shows that a Boolean logic modeling of analogical proportions can serve as a basis for solving quizzes as well as a common and popular type of IQ tests, namely Raven's progressive matrices. They are nonverbal tests supposedly measuring general intelligence. A 3 × 3 Raven matrix exhibits eight geometric pictures displayed as its eight first cells: the remaining ninth cell is empty. In these tests, a set of candidate pictures is also given among which the subject is asked to identify the solution. In this paper, we investigate a general approach allowing to automatically solve Raven's progressive matrices tests. The approach is based on a logical view of analogical proportions, i.e., statements of the form "A is to B as C is to D." We assume that analogical proportions hold between the rows and between the columns of the Raven's matrix. This view can be applied to a feature-based description of the pictures but also, in a number of cases, to a very low level representation, i.e., the pixel level. It appears that the analogical proportion reading just amounts here to a recopy of patterns of feature values that already appear in the data, after checking that there is no conflicting patterns. Implementing this principle, our algorithm builds up the ninth picture, without the help of any set of candidate solutions, and only on the basis of the eight known cells of the Raven matrices. A comparison with other approaches is provided. The ability to construct the missing picture without relying on candidate solutions is a distinctive feature of our work. Moreover, we emphasize the general principle underlying the approach that offers a simple and uniform mechanism applicable to the tests. At this step, the paper makes no claim about the cognitive validity of the approach with respect to the way humans solve such tests. C 2016 Wiley Periodicals, Inc.Indeed, a and b are supposed to be the values of a given binary feature for two distinct items. Then, a ∧ b holds if the two items have this feature in common, a ∧ b holds if none of the items has this feature, a ∧ b holds if the first item has the feature alone, and vice versa for a ∧ b.Generally speaking, a logical proportion 15 is a conjunction of two equivalences between such indicators. Among the 120 distinct logical proportions that exist, the In the above definition of an analogical proportion, a, b, c, and d belong to the same domain, namely, the set of truth values {0, 1}. We may need a view of analogy where a, b, c, and d do not belong to a unique universe. An easy way to do this is to state that an analogical proportion holds between a, b, c, and d as soon as there exists a relation R such that R(a, b) = R (c, d)

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Heuristic-Driven Theory Projection: An Overview

Cited by 17 publications

References 18 publications

Algorithmic Aspects of Theory Blending

Algorithmic Aspects of Theory Blending

Choosing the Right Path: Image Schema Theory as a Foundation for Concept Invention

Constructive Solving of Raven's IQ Tests with Analogical Proportions

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