950 research outputs found
A Denotational Semantics for First-Order Logic
In Apt and Bezem [AB99] (see cs.LO/9811017) we provided a computational
interpretation of first-order formulas over arbitrary interpretations. Here we
complement this work by introducing a denotational semantics for first-order
logic. Additionally, by allowing an assignment of a non-ground term to a
variable we introduce in this framework logical variables.
The semantics combines a number of well-known ideas from the areas of
semantics of imperative programming languages and logic programming. In the
resulting computational view conjunction corresponds to sequential composition,
disjunction to ``don't know'' nondeterminism, existential quantification to
declaration of a local variable, and negation to the ``negation as finite
failure'' rule. The soundness result shows correctness of the semantics with
respect to the notion of truth. The proof resembles in some aspects the proof
of the soundness of the SLDNF-resolution.Comment: 17 pages. Invited talk at the Computational Logic Conference (CL
2000). To appear in Springer-Verlag Lecture Notes in Computer Scienc
Semantic Domains and Denotational Semantics
The theory of domains was established in order to have appropriate spaces on which to define semantic functions for the denotational approach to programming-language semantics. There were two needs: first, there had to be spaces of several different types available to mirror both the type distinctions in the languages and also to allow for different kinds of semantical constructs - especially in dealing with languages with side effects; and second, the theory had to account for computability properties of functions - if the theory was going to be realistic. The first need is complicated by the fact that types can be both compound (or made up from other types) and recursive (or self-referential), and that a high-level language of types and a suitable semantics of types is required to explain what is going on. The second need is complicated by these complications of the semantical definitions and the fact that it has to be checked that the level of abstraction reached still allows a precise definition of computability
Sequentiality vs. Concurrency in Games and Logic
Connections between the sequentiality/concurrency distinction and the
semantics of proofs are investigated, with particular reference to games and
Linear Logic.Comment: 35 pages, appeared in Mathematical Structures in Computer Scienc
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