Related papers: A Game-Semantic Model of Computation
We present a logical framework that enables us to define a formal theory of computational trust in which this notion is analysed in terms of epistemic attitudes towards the possible objects of trust and in relation to existing evidence in…
Prior research has explored potential applications of video games in programming education to elicit computational thinking skills. However, existing approaches are often either too general, not taking into account the diversity of genres…
Historically, the notion of effective algorithm is closely related to the Church-Turing thesis. But effectivity imposes no restriction on computation time or any other resource; in that sense, it is incompatible with engineering or physics.…
Computability logic (CL) is a systematic formal theory of computational tasks and resources, which, in a sense, can be seen as a semantics-based alternative to (the syntactically introduced) linear logic. With its expressive and flexible…
Computation plays a major role in decision making. Even if an agent is willing to ascribe a probability to all states and a utility to all outcomes, and maximize expected utility, doing so might present serious computational problems.…
We refine HO/N game semantics with an additional notion of pointer (mu-pointers) and extend it to first-order classical logic with completeness results. We use a Church style extension of Parigot's lambda-mu-calculus to represent proofs of…
In this paper, we argue that simulation platforms enable a novel type of embodied spatial reasoning, one facilitated by a formal model of object and event semantics that renders the continuous quantitative search space of an open-world,…
We introduce a natural Turing-complete extension of first-order logic FO. The extension adds two novel features to FO. The first one of these is the capacity to add new points to models and new tuples to relations. The second one is the…
The field of computability and complexity was, where computer science sprung from. Turing, Church, and Kleene all developed formalisms that demonstrated what they held "intuitively computable". The times change however and today's…
Unlike computation or the numerical analysis of differential equations, simulation does not have a well established conceptual and mathematical foundation. Simulation is an arguable unique union of modeling and computation. However,…
We define a game semantics for second order classical arithmetic PA2 (with quantifiers over predicates on integers and full comprehension axiom). Our semantics is effective: moves are described by a finite amount of information and whenever…
In this vision paper, we explore the challenges and opportunities of a form of computation that employs an empirical (rather than a formal) approach, where the solution of a computational problem is returned as empirically most likely…
For over a decade, the hypercomputation movement has produced computational models that in theory solve the algorithmically unsolvable, but they are not physically realizable according to currently accepted physical theories. While…
We investigate the computational properties of basic mathematical notions pertaining to $\mathbb{R}\rightarrow \mathbb{R}$-functions and subsets of $\mathbb{R}$, like finiteness, countability, (absolute) continuity, bounded variation,…
We provide a compositional coalgebraic semantics for strategic games. In our framework, like in the semantics of functional programming languages, coalgebras represent the observable behaviour of systems derived from the behaviour of the…
Game semantics is a powerful method of semantic analysis for programming languages. It gives mathematically accurate models ("fully abstract") for a wide variety of programming languages. Game semantic models are combinatorial…
Cirquent calculus is a proof system with inherent ability to account for sharing subcomponents in logical expressions. Within its framework, this article constructs an axiomatization CL18 of the basic propositional fragment of computability…
The aim of this paper is to present an elementary computable theory of random variables, based on the approach to probability via valuations. The theory is based on a type of lower-measurable sets, which are controlled limits of open sets,…
Computability logic (CoL) (see http://www.cis.upenn.edu/~giorgi/cl.html) is a recently introduced semantical platform and ambitious program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth…
Game theoretic equilibria are mathematical expressions of rationality. Rational agents are used to model not only humans and their software representatives, but also organisms, populations, species and genes, interacting with each other and…