An order-sorted logic for knowledge representation systems

Bierle, C.; Hedtstück, Ulrich; Pletat, Udo; Schmitt, Peter H.; Siekmann, Jörg H.

doi:10.1016/0004-3702(92)90055-3

Cited by 54 publications

(41 citation statements)

References 18 publications

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“…(Frisch 1991 does not have a notion of well-sorted formula, but uses a similaralbeit weaker-notion of well-sorted substitution.) There is again a difference in the fact that sorts are in the language, contrary to much of the previous work (see, e.g., Walther 1987;Frisch 1991;Schmidt-Schauss 1989), but similarly to Weidenbach (1991Weidenbach ( , 1993a, Beierle et al (1992), and Cohn (1987).…”

Section: A Sorted Logic For Interactive Theorem Provingcontrasting

confidence: 51%

A Many‐Sorted Natural Deduction

Cimatti

Giunchiglia

Weyhrauch³

1998

Computational Intelligence

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The goal of this paper is to motivate and define yet another sorted logic, called SND. All the previous sorted logics that can be found in the Artificial Intelligence literature have been designed to be used in (completely) automated deduction. SND has been designed to be used in interactive theorem proving. Because of this shift of focus, SND has been designed to satisfy three innovative design requirements: it is defined on top of a natural deduction calculus, and in a way to be a definitional extension of such calculus; and it is implemented on top of its implementation. In turn, because of this fact, SND has various innovative technical properties; among them: it allows us to deal with free variables, it has no notion of well‐sortedness and of well‐sortedness being a prerequisite of well‐formedness, its implementation is such that, in the default mode, the system behaves exactly as with the original unsorted calculus.

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Section: A Sorted Logic For Interactive Theorem Provingcontrasting

confidence: 51%

A Many‐Sorted Natural Deduction

Cimatti

Giunchiglia

Weyhrauch³

1998

Computational Intelligence

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“…There is a waste literature on order-sorted logic and its applications in automated reasoning and knowledge representation (see, for instance, [35,34,5,14,23,36]). …”

Section: Encoding In Order-sorted Logicmentioning

confidence: 99%

Predicate Logic with Sequence Variables and Sequence Function Symbols

Kutsia

Buchberger

2004

Lecture Notes in Computer Science

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Abstract. We describe an extension of first-order logic with sequence variables and sequence functions. We define syntax, semantics and inference system for the extension so that Completeness, Compactness, Löwenheim-Skolem, and Model Existence theorems remain valid. The obtained logic can be encoded as a special order-sorted first-order theory. We also define an inductive theory with sequence variables and formulate induction rules. The calculus forms a basis for the top-down systematic theory exploration paradigm.

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“…On the other hand, we also use the sort processor within the inference engine, e.g., during the unification process, when the compatibility between the sort of a variable and the sort of a term that is to be substituted for the variable must be checked. Processing the sort literals (those literals whose predicate is a sort expression) also requires us to invoke the sort processor to check whether a sort literal can be eliminated [47].…”

Section: Logic Interfacementioning

confidence: 99%

Knowledge in operation

Bollinger

Pletat

1992

IBM J. Res. & Dev.

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The L^LOG knowledge representation language and an inference engine to interpret It have been developed as part of the LI LOG project, where new concepts for understanding natural-language texts were investigated. L^^^Q is a typed predicate logic whose type system has adopted the concepts of KL-One-like languages. Further language constructs allow the formulation of default and control knowledge. The inference engine for L^,^QQ was designed as an experimental theorem prover, allowing us to Investigate the behavior of various inference calculi as well as a number of search strategies. Processing with L^,^QQ is not restricted to a prepositional reasoner for logical formulas; we are also able to delegate special kinds of inferences to external deductive components. Currently, one such external reasoner for processing spatial information on the basis of analog representation Is attached to the inference engine.

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An order-sorted logic for knowledge representation systems

Cited by 54 publications

References 18 publications

A Many‐Sorted Natural Deduction

A Many‐Sorted Natural Deduction

Predicate Logic with Sequence Variables and Sequence Function Symbols

Knowledge in operation

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