Related papers: Intensionality, Definability and Computation
We discuss how mathematical semantics has evolved, and suggest some new directions for future work. As an example, we discuss some recent work on encapsulating model comparison games as comonads, in the context of finite model theory.
We develop methods to formally describe and compare games, in order to probe questions of game structure and design, and as a stepping stone to predicting player behavior from design patterns. We define a grammar-like formalism to describe…
We examine the meaning and the complexity of probabilistic logic programs that consist of a set of rules and a set of independent probabilistic facts (that is, programs based on Sato's distribution semantics). We focus on two semantics,…
Compositionality is a key property for dealing with complexity, which has been studied from many points of view in diverse fields. Particularly, the composition of individual computations (or programs) has been widely studied almost since…
We define a model for linear logic based on two well-known ingredients: games and simulations. This model is interesting in the following respect: while it is obvious that the objects interpreting formulas are games and that everything is…
The benchmark for computation is typically given as Turing computability; the ability for a computation to be performed by a Turing Machine. Many languages exploit (indirect) encodings of Turing Machines to demonstrate their ability to…
This work extends the present author's computational game semantics of Martin-L\"{o}f type theory to the cumulative hierarchy of universes. This extension completes game semantics of all standard types of Martin-L\"{o}f type theory for the…
We discuss partial specifications in first-order logic FO and also in a Turing-complete extension of FO. We compare the compositional and game-theoretic approaches to the systems.
We study the semantic foundation of expressive probabilistic programming languages, that support higher-order functions, continuous distributions, and soft constraints (such as Anglican, Church, and Venture). We define a metalanguage (an…
By paying more attention to semantics-based tool generation, programming language semantics can significantly increase its impact. Ultimately, this may lead to ``Language Design Assistants'' incorporating substantial amounts of semantic…
The aim of this of this paper is to study infinite games and to prove formally some properties in this framework. As a consequence we show that the behavior (the madness) of people which leads to speculative crashes or escalation can be…
Game semantics extends the Curry-Howard isomorphism to a three-way correspondence: proofs, programs, strategies. But the universe of strategies goes beyond intuitionistic logics and lambda calculus, to capture stateful programs. In this…
This is an introduction to Game Semantics based on some lecture notes given at the CLiCS II summer school in Cambridge in 1995. We will focus on the recent (1994) work on Game semantics, which has led to some striking advances in the Full…
I consider issues in distributed computation that should be of relevance to game theory. In particular, I focus on (a) representing knowledge and uncertainty, (b) dealing with failures, and (c) specification of mechanisms.
While event handling is a key element in modern interactive programming, it is unfortunate that its theoretical foundation is rather weak. To solve this problem, we propose to adopt a game-logical approach of computability logic…
Formal semantics offers a complete and rigorous definition of a language. It is important to define different semantic models for a language and different models serve different purposes. Building equivalence between different semantic…
We have proposed going beyond traditional ontologies to use rich semantics implemented in programming languages for modeling. In this paper, we discuss the application of executable semantic models to two examples, first a structured…
The article bridges between two major paradigms in computation, the functional, at basis computation from input to output, and the interactive, where computation reacts to its environment while underway. Central to any compositional theory…
The semantic technologies pose new challenge for the way in which we built and operate systems. They are tools used to represent significances, associations, theories, separated from data and code. Their goal is to create, to discover, to…
We consider discrete-time uncertain processes with finite state space and study the properties of game-theoretic upper expectations developed by Shafer and Vovk. We start by proving some basic properties, e.g. monotonicity, law of iterated…