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Connectionist Model generation: A FirstOrder Approach
, 2007
"... Knowledge based artificial neural networks have been applied quite successfully to propositional knowledge representation and reasoning tasks. However, as soon as these tasks are extended to structured objects and structuresensitive processes as expressed e.g., by means of firstorder predicate log ..."
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Cited by 20 (5 self)
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Knowledge based artificial neural networks have been applied quite successfully to propositional knowledge representation and reasoning tasks. However, as soon as these tasks are extended to structured objects and structuresensitive processes as expressed e.g., by means of firstorder predicate logic, it is not obvious at all what neural symbolic systems would look like such that they are truly connectionist, are able to learn, and allow for a declarative reading and logical reasoning at the same time. The core method aims at such an integration. It is a method for connectionist model generation using recurrent networks with feedforward core. We show in this paper how the core method can be used to learn firstorder logic programs in a connectionist fashion, such that the trained network is able to do reasoning over the acquired knowledge. We also report on experimental evaluations which show the feasibility of our approach.
The core method: Connectionist model generation
 In Proceedings of the 16th International Conference on Artificial Neural Networks (ICANN
, 2006
"... Abstract. Knowledge based artificial networks networks have been applied quite successfully to propositional knowledge representation and reasoning tasks. However, as soon as these tasks are extended to structured objects and structuresensitive processes it is not obvious at all how neural symbol ..."
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Cited by 9 (4 self)
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Abstract. Knowledge based artificial networks networks have been applied quite successfully to propositional knowledge representation and reasoning tasks. However, as soon as these tasks are extended to structured objects and structuresensitive processes it is not obvious at all how neural symbolic systems should look like such that they are truly connectionist and allow for a declarative reading at the same time. The core method aims at such an integration. It is a method for connectionist model generation using recurrent networks with feedforward core. After an introduction to the core method, this paper will focus on possible connectionist representations of structured objects and their use in structuresensitive reasoning tasks. 1
2009c. Logics and networks for human reasoning
 In ICANN’09
"... Abstract We propose to model human reasoning tasks using completed logic programs interpreted under the threevalued Lukasiewicz semantics. Given an appropriate immediate consequence operator, completed logic programs admit a least model, which can be computed by iterating the consequence operator. ..."
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Cited by 6 (3 self)
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Abstract We propose to model human reasoning tasks using completed logic programs interpreted under the threevalued Lukasiewicz semantics. Given an appropriate immediate consequence operator, completed logic programs admit a least model, which can be computed by iterating the consequence operator. Reasoning is then performed with respect to the least model. The approach is realized in a connectionist setting.
Connectionist Representation of MultiValued Logic Programs
"... Hölldobler and Kalinke showed how, given a propositional logic program P, a 3layer feedforward artificial neural network may be constructed, using only binary threshold units, which can compute the familiar immediateconsequence operator TP associated with P. In this chapter, essentially these res ..."
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Cited by 3 (3 self)
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Hölldobler and Kalinke showed how, given a propositional logic program P, a 3layer feedforward artificial neural network may be constructed, using only binary threshold units, which can compute the familiar immediateconsequence operator TP associated with P. In this chapter, essentially these results are established for a class of logic programs which can handle manyvalued logics, constraints and uncertainty; these programs therefore represent a considerable extension of conventional propositional programs. The work of the chapter basically falls into two parts. In the first of these, the programs considered extend the syntax of conventional logic programs by allowing elements of quite general algebraic structures to be present in clause bodies. Such programs include manyvalued logic programs, and semiringbased constraint logic programs. In the second part, the programs considered are bilatticebased annotated logic programs in which body literals are annotated by elements drawn from bilattices. These programs are wellsuited to handling uncertainty. Appropriate semantic operators are defined for the programs considered in both parts of the chapter, and it is shown that one may construct
Title: Logic Programs and ThreeValued Consequence Operators
, 2009
"... I hereby declare that this thesis is my own work, only with the help of the referenced literature and under the careful supervision of my thesis supervisor. ..."
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I hereby declare that this thesis is my own work, only with the help of the referenced literature and under the careful supervision of my thesis supervisor.
Some Properties of General Semantic Operators
"... We discuss a very general semantic operator arising within logicbased programming systems from an algebraic point of view, and show how it connects four interesting aspects of computation: neural networks, conventional logic programming, constraint logic programming, and a simple model of uncertai ..."
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We discuss a very general semantic operator arising within logicbased programming systems from an algebraic point of view, and show how it connects four interesting aspects of computation: neural networks, conventional logic programming, constraint logic programming, and a simple model of uncertainty in logicbased systems.
Connectionist Model Generation: A FirstOrder Approach
"... Knowledge based artificial neural networks have been applied quite successfully to propositional knowledge representation and reasoning tasks. However, as soon as these tasks are extended to structured objects and structuresensitive processes as expressed e.g., by means of firstorder predicate log ..."
Abstract
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Knowledge based artificial neural networks have been applied quite successfully to propositional knowledge representation and reasoning tasks. However, as soon as these tasks are extended to structured objects and structuresensitive processes as expressed e.g., by means of firstorder predicate logic, it is not obvious at all what neural symbolic systems would look like such that they are truly connectionist, are able to learn, and allow for a declarative reading and logical reasoning at the same time. The core method aims at such an integration. It is a method for connectionist model generation using recurrent networks with feedforward core. We show in this paper how the core method can be used to learn firstorder logic programs in a connectionist fashion, such that the trained network is able to do reasoning over the acquired knowledge. We
Properties of General Semantic Operators Determined by LogicBased Systems
"... We discuss a very general semantic operator arising within logicbased programming systems from an algebraic point of view, and show how it connects four interesting aspects of computation: neural networks, conventional logic programming, constraint logic programming, and simple models of uncertaint ..."
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We discuss a very general semantic operator arising within logicbased programming systems from an algebraic point of view, and show how it connects four interesting aspects of computation: neural networks, conventional logic programming, constraint logic programming, and simple models of uncertainty in logicbased systems.