Nondeterminism in Algebraic Specifications and Algebraic Programs

Hußmann, Heinrich

doi:10.1007/978-1-4684-6834-2

Cited by 34 publications

(47 citation statements)

References 8 publications

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“…propositional fragment, second order extension, etc. A similar result is shown for a rather natural fuzzy extension of the multi-algebras framework [23,24,35,36].…”

Section: Introductionsupporting

confidence: 78%

“…In this section we show that two important concrete mvl systems, namely traditional first order mvl (MVL) and a fuzzy extension of multi-algebras (of [23,24,35,36]), may be embedded conservatively into our abstract mvl framework I(L). These are embeddings both at the syntactic and at the semantic level.…”

Section: Embedding Concrete Many-valued Institutions Into I(l)mentioning

confidence: 99%

“…Multi-algebras have been introduced as an algebraic specification framework for non-determinism [23,35,36] and later on developed as a general framework for algebraic specification [24]. Lamo's thesis [24] shows that multi-algebras subsume important algebraic formalisms used in formal specification such as partial algebra [4] and membership algebra [28].…”

Section: Fuzzy Multi-algebrasmentioning

confidence: 99%

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Institutional semantics for many-valued logics

Diaconescu

2013

Fuzzy Sets and Systems

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We develop many-valued logic, including a generic abstract model theory, over a fully abstract syntax. We show that important many-valued logic model theories, such as traditional first-order many-valued logic and fuzzy multi-algebras, may be conservatively embedded into our abstract framework. Our development is technically based upon the so-called theory of institutions of Goguen and Burstall and may serve as a template for defining at hand many-valued logic model theories over various concrete syntaxes or, from another perspective, to combine many-valued logic with other logical systems. We also show that our generic many-valued logic abstract model theory enjoys a couple of important institutional model theory properties that support the development of deep model theory methods.

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“…propositional fragment, second order extension, etc. A similar result is shown for a rather natural fuzzy extension of the multi-algebras framework [23,24,35,36].…”

Section: Introductionsupporting

confidence: 78%

Section: Embedding Concrete Many-valued Institutions Into I(l)mentioning

confidence: 99%

Section: Fuzzy Multi-algebrasmentioning

confidence: 99%

See 1 more Smart Citation

Institutional semantics for many-valued logics

Diaconescu

2013

Fuzzy Sets and Systems

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“…Multi-algebras have been introduced as an algebraic specification framework for non-determinism [26,41,42] and later on developed as a general framework for algebraic specification [27]. Lamo's thesis [27] shows that multi-algebras subsume important algebraic formalisms used in formal specification such as partial algebra [3] and membership algebra [31].…”

Section: Example 43 (Horn Many-valued Logic)mentioning

confidence: 99%

Graded consequence: an institution theoretic study

Diaconescu

2014

Soft Comput

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We develop a general study of graded consequence (of many-valued logic) in an institution theoretic (in the sense of Goguen and Burstall) style. This means both syntax and semantics are considered fully abstract, as well as the satisfaction between them. Our approach contrasts to other approaches on many-valued logic in that it is a multisignature one, in the spirit of institution theory. We consider graded consequence at three different conceptual levels: entailment, semantic, and closure operators, and explore several interpretations between them. We also study logical connectors and quantifiers both at the entailment and semantic level, compactness and soundness properties.

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“…This behavior corresponds to call-time choice [17,11], the semantics for nondeterminism adopted by those systems. Operationally call-time choice is very close to the sharing mechanism used in functional languages to implement lazy evaluation.…”

Section: Introductionmentioning

confidence: 99%

Rewriting and Call-Time Choice: The HO Case

López-Fraguas¹,

Rodríguez-Hortalá²,

Sánchez-Hernández³

Functional and Logic Programming

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Abstract. It is known that the behavior of non-deterministic functions with call-time choice semantics, present in current functional logic languages, is not well described by ordinary approaches to reduction like ordinary term rewriting systems or λ-calculus. The presence of HO features makes things more difficult, since reasoning principles that are essential in a standard (i.e., deterministic) functional setting, like extensionality, become wrong. In this paper we propose HOlet-rewriting, a notion of rewriting with local bindings that turns out to be adequate for programs with HO non-deterministic functions, as it is shown by strong equivalence results with respect to HOCRWL, a previously existing semantic framework for such programs. In addition, we give a sound and complete notion of HOlet-narrowing, we show by a case study the usefulness of the achieved combination of semantic and reduction notions, and finally we prove within our framework that a standard approach to the implementation of HO features, namely translation to FO, is still valid for HO nondeterministic functions.

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Nondeterminism in Algebraic Specifications and Algebraic Programs

Cited by 34 publications

References 8 publications

Institutional semantics for many-valued logics

Institutional semantics for many-valued logics

Graded consequence: an institution theoretic study

Rewriting and Call-Time Choice: The HO Case

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