An interactive semantics of logic programming

We apply to logic programming some recently emerging ideas from the field of reduction-based communicating systems, with the aim of giving evidence of the hidden interactions and the coordination mechanisms that rule the operational machinery of such a programming paradigm. The semantic framework we have chosen for presenting our results is tile logic, which has the advantage of allowing a uniform treatment of goals and observations and of applying abstract categorical tools for proving the results. As main contributions, we mention the finitary presentation of abstract unification, and a concurrent and coordinated abstract semantics consistent with the most common semantics of logic programming. Moreover, the compositionality of the tile semantics is guaranteed by standard results, as it reduces to check that the tile systems associated to logic programs enjoy the tile decomposition property. An extension of the approach for handling constraint systems is also discussed.Comment: 42 pages, 24 figure, 3 tables, to appear in the CUP journal of Theory and Practice of Logic Programmin

Interactive semantics

Much research pursues machine intelligence through better representation of semantics. What is semantics? People in different areas view semantics from different facets although it accompanies interaction through civilization. Some researchers believe that humans have some innate structure in mind for processing semantics. Then, what the structure is like? Some argue that humans evolve a structure for processing semantics through constant learning. Then, how the process is like? Humans have invented various symbol systems to represent semantics. Can semantics be accurately represented? Turing machines are good at processing symbols according to algorithms designed by humans, but they are limited in ability to process semantics and to do active interaction. Super computers and high-speed networks do not help solve this issue as they do not have any semantic worldview and cannot reflect themselves. Can future cyber-society have some semantic images that enable machines and individuals (humans and agents) to reflect themselves and interact with each other with knowing social situation through time? This paper concerns these issues in the context of studying an interactive semantics for the future cyber-society. It firstly distinguishes social semantics from natural semantics, and then explores the interactive semantics in the category of social semantics. Interactive semantics consists of an interactive system and its semantic image, which co-evolve and influence each other. The semantic worldview and interactive semantic base are proposed as the semantic basis of interaction. The process of building and explaining semantic image can be based on an evolving structure incorporating adaptive multi-dimensional classification space and self-organized semantic link network. A semantic lens is proposed to enhance the potential of the structure and help individuals build and retrieve semantic images from different facets, abstraction levels and scales through time

Infinitary Classical Logic: Recursive Equations and Interactive Semantics

In this paper, we present an interactive semantics for derivations in an infinitary extension of classical logic. The formulas of our language are possibly infinitary trees labeled by propositional variables and logical connectives. We show that in our setting every recursive formula equation has a unique solution. As for derivations, we use an infinitary variant of Tait-calculus to derive sequents. The interactive semantics for derivations that we introduce in this article is presented as a debate (interaction tree) between a test > (derivation candidate, Proponent) and an environment << not S >> (negation of a sequent, Opponent). We show a completeness theorem for derivations that we call interactive completeness theorem: the interaction between > (test) and > (environment) does not produce errors (i.e., Proponent wins) just in case > comes from a syntactical derivation of >.Comment: In Proceedings CL&C 2014, arXiv:1409.259

Resumptions, Weak Bisimilarity and Big-Step Semantics for While with Interactive I/O: An Exercise in Mixed Induction-Coinduction

We look at the operational semantics of languages with interactive I/O through the glasses of constructive type theory. Following on from our earlier work on coinductive trace-based semantics for While, we define several big-step semantics for While with interactive I/O, based on resumptions and termination-sensitive weak bisimilarity. These require nesting inductive definitions in coinductive definitions, which is interesting both mathematically and from the point-of-view of implementation in a proof assistant. After first defining a basic semantics of statements in terms of resumptions with explicit internal actions (delays), we introduce a semantics in terms of delay-free resumptions that essentially removes finite sequences of delays on the fly from those resumptions that are responsive. Finally, we also look at a semantics in terms of delay-free resumptions supplemented with a silent divergence option. This semantics hinges on decisions between convergence and divergence and is only equivalent to the basic one classically. We have fully formalized our development in Coq.Comment: In Proceedings SOS 2010, arXiv:1008.190

Coinductive Big-Step Semantics for Concurrency

In a paper presented at SOS 2010, we developed a framework for big-step semantics for interactive input-output in combination with divergence, based on coinductive and mixed inductive-coinductive notions of resumptions, evaluation and termination-sensitive weak bisimilarity. In contrast to standard inductively defined big-step semantics, this framework handles divergence properly; in particular, runs that produce some observable effects and then diverge, are not "lost". Here we scale this approach for shared-variable concurrency on a simple example language. We develop the metatheory of our semantics in a constructive logic.Comment: In Proceedings PLACES 2013, arXiv:1312.221