Fixed point theorems and semantics: a folk tale

Lassez, Jean-Louis; Nguyễn, Văn Kính; Sonenberg, Ea

doi:10.1016/0020-0190(82)90065-5

Cited by 106 publications

(50 citation statements)

References 12 publications

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“…We call this transformer F [17], [18] gives an even stronger result than mere existence of a least fixed point. It states that this least fixed point can be constructed in ω steps by iterated application of F ξ C ′ f to the least element 0, i.e.…”

Section: Non-negative Weakest Pre-expectationsmentioning

confidence: 99%

A weakest pre-expectation semantics for mixed-sign expectations

Kaminski

Katoen

2017

2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

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Abstract-We present a weakest-precondition-style calculus for reasoning about the expected values (pre-expectations) of mixed-sign unbounded random variables after execution of a probabilistic program. The semantics of a while-loop is defined as the limit of iteratively applying a functional to a zero-element just as in the traditional weakest pre-expectation calculus, even though a standard least fixed point argument is not applicable in our semantics. A striking feature of our semantics is that it is always well-defined, even if the expected values do not exist. We show that the calculus is sound and allows for compositional reasoning. Furthermore, we present an invariant-based approach for reasoning about pre-expectations of loops.

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Section: Non-negative Weakest Pre-expectationsmentioning

confidence: 99%

A weakest pre-expectation semantics for mixed-sign expectations

Kaminski

Katoen

2017

2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

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“…We need to use the following (well known) results on fixed points originally due to Tarski and Kleene [14]. Proposition 3.14 Let U, ≤ be a complete lattice, u ∈ U and f : U → U a monotonic map such that u ≤ f (u).…”

Section: Unconstrained Fibringmentioning

confidence: 99%

Fibring of logics as a categorial construction

Sernadas

Caleiro

1999

Journal of Logic and Computation

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Much attention has been given recently to the mechanism of fibring of logics, allowing free mixing of the connectives and using proof rules from both logics. Fibring seems to be a rather useful and general form of combination of logics that deserves detailed study. It is now well understood at the proof-theoretic level. However, the semantics of fibring is still insufficiently understood. Herein we provide a categorial definition of both proof-theoretic and model-theoretic fibring for logics without terms. To this end, we introduce the categories of Hilbert calculi, interpretation systems and logic system presentations. By choosing appropriate notions of morphism it is possible to obtain pure fibring as a coproduct. Fibring with shared symbols is then easily obtained by cocartesian lifting from the category of signatures. Soundness is shown to be preserved by these constructions. We illustrate the constructions within propositional modal logic.

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“…The following is the text of an invited lecture for the LICS 2005 meeting held in Chicago June [26][27][28][29]2005. 1 Almost exactly eight years ago today, Anita Feferman gave a lecture for LICS 1997 at the University of Warsaw with the title, "The saga of Alfred Tarski: From Warsaw to Berkeley."…”

Section: Solomon Fefermanmentioning

confidence: 99%

Tarski's influence on computer science

Feferman¹

2006

Logical Methods in Computer Science

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Abstract. Alfred Tarski's influence on computer science was indirect but significant in a number of directions and was in certain respects fundamental. Here surveyed is Tarski's work on the decision procedure for algebra and geometry, the method of elimination of quantifiers, the semantics of formal languages, model-theoretic preservation theorems, and algebraic logic; various connections of each with computer science are taken up.

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Fixed point theorems and semantics: a folk tale

Cited by 106 publications

References 12 publications

A weakest pre-expectation semantics for mixed-sign expectations

A weakest pre-expectation semantics for mixed-sign expectations

Fibring of logics as a categorial construction

Tarski's influence on computer science

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