Conceptual structures: information processing in mind and machine
Conceptual structures: information processing in mind and machine
Logic for computer science: foundations of automatic theorem proving
Logic for computer science: foundations of automatic theorem proving
An algebraic semantics approach to the effective resolution of type equations
Theoretical Computer Science
Explicit representation of terms defined by counter examples
Journal of Automated Reasoning
Foundations of logic programming; (2nd extended ed.)
Foundations of logic programming; (2nd extended ed.)
Principles of database and knowledge-base systems, Vol. I
Principles of database and knowledge-base systems, Vol. I
Quantifying inductive bias: AI learning algorithms and Valiant's learning framework
Artificial Intelligence
Lecture notes in computer science on Foundations of logic and functional programming
POPL '91 Proceedings of the 18th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A Polynomial Approach to the Constructive Induction of Structural Knowledge
Machine Learning - Special issue on evaluating and changing representation
Algebraic Semantics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Version spaces: a candidate elimination approach to rule learning
IJCAI'77 Proceedings of the 5th international joint conference on Artificial intelligence - Volume 1
Induction of concepts in the predicate calculus
IJCAI'75 Proceedings of the 4th international joint conference on Artificial intelligence - Volume 1
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Signatures, as introduced to cope with semantics of programming languages, provide an interesting framework for knowledge representation. They allow structured and recursive properties that attribute representation does not permit, and at the same time seem to be algorithmically treatable. We recall how a generalisation relation on terms can be introduced by means of the classical special symbol Ω, whose meaning is “indeterminate”, and the partial order inductively defined on the terms. This formalism can nevertheless not take into account negation or disjunction. We provide in this paper a generalisation relation on sets of terms to withdraw these restrictions. This relation has different definitions (syntactical, set-theoretic, and based on a closed world assumption) that are proved to be equivalent for specific classes of signatures. They yield an equivalence relation whose canonical form is studied. We also study the combinatorial and algorithmic issues of the generalisation relation: the following problems are proved to be decidable (on finite data) but generally at least NP-complete: Does set A generalise set B? Are sets A and B equivalent? Is set B the canonical form of set A? Compute the negation of set A.... In the case where one of the sets contains only terms maximal for the generalisation relation, the first three problems are shown to be polynomial.