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Jan A. Bergstra [7]Jan Bergstra [6]
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Jan A. Bergstra
University of Amsterdam
  1.  25
    Logic of Transition Systems.Johan Van Benthem & Jan Bergstra - 1994 - Journal of Logic, Language and Information 3 (4):247-283.
    Labeled transition systems are key structures for modeling computation. In this paper, we show how they lend themselves to ordinary logical analysis (without any special new formalisms), by introducing their standard first-order theory. This perspective enables us to raise several basic model-theoretic questions of definability, axiomatization and preservation for various notions of process equivalence found in the computational literature, and answer them using well-known logical techniques (including the Compactness theorem, Saturation and Ehrenfeucht games). Moreover, we consider what happens to this (...)
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  2.  41
    A Propositional Logic with 4 Values: True, False, Divergent and Meaningless.Jan A. Bergstra, Inge Bethke & Piet Rodenburg - 1995 - Journal of Applied Non-Classical Logics 5 (2):199-217.
  3.  20
    Logic of Transition Systems.Johan Benthem & Jan Bergstra - 1994 - Journal of Logic, Language and Information 3 (4):247-283.
    Labeled transition systems are key structures for modeling computation. In this paper, we show how they lend themselves to ordinary logical analysis (without any special new formalisms), by introducing their standard first-order theory. This perspective enables us to raise several basic model-theoretic questions of definability, axiomatization and preservation for various notions of process equivalence found in the computational literature, and answer them using well-known logical techniques (including the Compactness theorem, Saturation and Ehrenfeucht games). Moreover, we consider what happens to this (...)
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  4.  10
    Equations for Formally Real Meadows.Jan A. Bergstra, Inge Bethke & Alban Ponse - 2015 - Journal of Applied Logic 13 (2):1-23.
  5.  17
    Bochvar-McCarthy Logic and Process Algebra.Jan A. Bergstra & Alban Ponse - 1998 - Notre Dame Journal of Formal Logic 39 (4):464-484.
    We propose a combination of Bochvar's strict three-valued logic, McCarthy's sequential three-valued logic, and process algebra via the conditional guard construct. This combination entails the introduction of a new constant meaningless in process algebra. We present an operational semantics in SOS-style, and a completeness result for ACP with conditional guard construct and the proposed logic.
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  6.  40
    Effective Transformations on Probabilistic Data.Jan Bergstra - 1979 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 25 (13-18):219-226.
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  7.  3
    Non-Commutative Propositional Logic with Short-Circuit Evaluation.Jan A. Bergstra, Alban Ponse & Daan J. C. Staudt - 2021 - Journal of Applied Non-Classical Logics 31 (3-4):234-278.
    Short-circuit evaluation denotes the semantics of propositional connectives in which the second argument is evaluated only if the first is insufficient to determine the value of the expression. Com...
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  8.  41
    Degrees of Sensible Lambda Theories.Henk Barendregt, Jan Bergstra, Jan Willem Klop & Henri Volken - 1978 - Journal of Symbolic Logic 43 (1):45-55.
    A λ-theory T is a consistent set of equations between λ-terms closed under derivability. The degree of T is the degree of the set of Godel numbers of its elements. H is the $\lamda$ -theory axiomatized by the set {M = N ∣ M, N unsolvable. A $\lamda$ -theory is sensible $\operatorname{iff} T \supset \mathscr{H}$ , for a motivation see [6] and [4]. In § it is proved that the theory H is ∑ 0 2 -complete. We present Wadsworth's proof (...)
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  9.  22
    Note on Paraconsistency and Reasoning About Fractions.Jan A. Bergstra & Inge Bethke - 2015 - Journal of Applied Non-Classical Logics 25 (2):120-124.
    We apply a paraconsistent strategy to reasoning about fractions.
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  10.  14
    Execution Architectures for Program Algebra.Jan A. Bergstra & Alban Ponse - 2007 - Journal of Applied Logic 5 (1):170-192.
  11.  15
    Discourse Between Processes.Jan Bergstra - 1980 - Notre Dame Journal of Formal Logic 21 (1):131-134.
  12.  13
    Degrees of Partial Functions.Jan Bergstra - 1978 - Notre Dame Journal of Formal Logic 19 (1):152-154.
  13.  11
    Process Algebra with Four-Valued Logic.Jan A. Bergstra & Alban Ponse - 2000 - Journal of Applied Non-Classical Logics 10 (1):27-53.
    ABSTRACT We propose a combination of a fragment of four-valued logic and process algebra. This fragment is geared to a simple relation with process algebra via the conditional guard construct, and can easily be extended to a truth-functionally complete logic. We present an operational semantics in SOS-style, and a completeness result for ACP with conditionals and four- valued logic. Completeness is preserved under the restriction to some other non-classical logics.
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