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

The Common Order-Theoretic Structure of Version Spaces and ATMS\u27s

This paper exposes the common order-theoretic properties of the structures manipulated by the version space algorithm [Mit78]and the assumption-based truth maintenance systems (ATMS) [dk86a,dk86b] by recasting them in the framework of convex spaces. Our analysis of version spaces in this framework reveals necessary and sufficient conditions for ensuring the preservation of an essential finite representability property in version space merging. This analysis is used to formulate several sufficient conditions for when a language will allow version spaces to be represented by finite sets of concepts (even when the universe of concepts may be infinite). We provide a new convex space based formulation of computation performs by an ATMS which extends the expressiveness of disjunctions in the systems. This approach obviates the need for hyper-resolution in dealing with disjunction and results in simpler label-update algorithms

A Semantics for Complex Objects and Approximate Answers

AbstractA new definition of complex objects is introduced which provides a denotation for incomplete tuples as well as partially described sets. Set values are “sandwiched” between “complete” and “consistent” descriptions (respectively represented in the Smyth and Hoare powerdomains), allowing the maximal values to be arbitrary subsets of maximal elements in the domain of the space of descriptions. We then restrict our attention to complex objects which are in some sense “natural,” i.e., those which represent “views” of entity-relationship databases, and define rules over these objects. The rules can be used not only as an integrity check on the information in the database, but can be used constructively to infer consistent instances of conclusions and to refine complete instances of the hypothesis. The system is shown to extend the power of datalog (without negation) and the relational algebra (with set difference), and to have an efficient implementation

A Fully Abstract Semantics for a Functional Language with Logic Variables

We present a novel denotational semantics for a functional language with logic variables intended for parallel execution. The intuition behind this semantics is that equations represent equational constraints on data. Thus, a system of equations can be viewed as defining a set of possibly inconsistent constraints. The semantics is couched in terms of closure operators on a Scott domain. This allows one to abstract away from all the complexities associated with operational reasoning expressed in terms of concurrent threads of execution. We define a structural operational semantics for the language that expresses precisely the concurrent execution model that we have in mind. We show that the abstract denotational semantics is fully abstract with respect to the operational semantics. This is surprising, given how very different the two semantic descriptions are. It also shows that thinking in terms of constraints is an accurate substitute for thinking in terms of explicit parallel execution. The proof of full abstraction is complicated by the fact that there are potentially infinite objects in the domain