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  1. An independent axiomatisation for free short-circuit logic.Alban Ponse & Daan J. C. Staudt - 2018 - Journal of Applied Non-Classical Logics 28 (1):35-71.
    Short-circuit evaluation denotes the semantics of propositional connectives in which the second argument is evaluated only if the first argument does not suffice to determine the value of the expression. Free short-circuit logic is the equational logic in which compound statements are evaluated from left to right, while atomic evaluations are not memorised throughout the evaluation, i.e. evaluations of distinct occurrences of an atom in a compound statement may yield different truth values. We provide a simple semantics for free short-circuit (...)
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  • Generalizing Functional Completeness in Belnap-Dunn Logic.Hitoshi Omori & Katsuhiko Sano - 2015 - Studia Logica 103 (5):883-917.
    One of the problems we face in many-valued logic is the difficulty of capturing the intuitive meaning of the connectives introduced through truth tables. At the same time, however, some logics have nice ways to capture the intended meaning of connectives easily, such as four-valued logic studied by Belnap and Dunn. Inspired by Dunn’s discovery, we first describe a mechanical procedure, in expansions of Belnap-Dunn logic, to obtain truth conditions in terms of the behavior of the Truth and the False, (...)
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  • 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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  • 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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  • 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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  • Inversive meadows and divisive meadows.J. A. Bergstra & C. A. Middelburg - 2011 - Journal of Applied Logic 9 (3):203-220.
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  • Execution architectures for program algebra.Jan A. Bergstra & Alban Ponse - 2007 - Journal of Applied Logic 5 (1):170-192.