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Full-Text Articles in Physical Sciences and Mathematics
Continuity Of Semantic Operators In Logic Programming And Their Approximation By Artificial Neural Networks, Pascal Hitzler, Anthony K. Seda
Continuity Of Semantic Operators In Logic Programming And Their Approximation By Artificial Neural Networks, Pascal Hitzler, Anthony K. Seda
Computer Science and Engineering Faculty Publications
One approach to integrating first-order logic programming and neural network systems employs the approximation of semantic operators by feedforward networks. For this purpose, it is necessary to view these semantic operators as continuous functions on the reals. This can be accomplished by endowing the space of all interpretations of a logic program with topologies obtained from suitable embeddings. We will present such topologies which arise naturally out of the theory of logic programming, discuss continuity issues of several well-known semantic operators, and derive some results concerning the approximation of these operators by feedforward neural networks.
Generalized Metrics And Uniquely Determined Logic Programs, Pascal Hitzler, Anthony K. Seda
Generalized Metrics And Uniquely Determined Logic Programs, Pascal Hitzler, Anthony K. Seda
Computer Science and Engineering Faculty Publications
The introduction of negation into logic programming brings the benefit of enhanced syntax and expressibility, but creates some semantical problems. Specifically, certain operators which are monotonic in the absence of negation become non-monotonic when it is introduced, with the result that standard approaches to denotational semantics then become inapplicable. In this paper, we show how generalized metric spaces can be used to obtain fixed-point semantics for several classes of programs relative to the supported model semantics, and investigate relationships between the underlying spaces we employ. Our methods allow the analysis of classes of programs which include the acyclic, locally hierarchical, …
Formal Concept Analysis And Resolution On Algebraic Domains - Preliminary Report, Matthias Wendt, Pascal Hitzler
Formal Concept Analysis And Resolution On Algebraic Domains - Preliminary Report, Matthias Wendt, Pascal Hitzler
Computer Science and Engineering Faculty Publications
We relate two formerly independent areas: Formal concept analysis and logic of domains. We will establish a correspondence between contextual attribute logic on formal contexts resp. concept lattices and a clausal logic on coherent algebraic cpos. We show how to identify the notion of formal concept in the domain theoretic setting. In particular, we show that a special instance of the resolution rule from the domain logic coincides with the concept closure operator from formal concept analysis. The results shed light on the use of contexts and domains for knowledge representation and reasoning purposes.