Related papers: A Game-Theoretic Computational Interpretation of P…
In the same sense as classical logic is a formal theory of truth, the recently initiated approach called computability logic is a formal theory of computability. It understands (interactive) computational problems as games played by a…
Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that appear in imprecise-probabilistic decision…
Computability logic (CoL) is a formal theory of interactive computation. It understands computational problems as games played by two players: a machine and its environment, uses logical formalism to describe valid principles of…
Extending G\"odel's \emph{Dialectica} interpretation, we provide a functional interpretation of classical theories of positive arithmetic inductive definitions, reducing them to theories of finite-type functionals defined using transfinite…
Interpretability has arisen as a key desideratum of machine learning models alongside performance. Approaches so far have been primarily concerned with fixed dimensional inputs emphasizing feature relevance or selection. In contrast, we…
A computation in the continuation monad returns a final result given a continuation, ie. it is a function with type $(X \to R) \to R$. If we instead return the intermediate result at $X$ then our computation is called a selection function.…
Game semantics and winning strategies offer a potential conceptual bridge between semantics and proof systems of logics. We illustrate this link for hybrid logic -- an extension of modal logic that allows for explicit reference to worlds…
Performance prediction or forecasting sporting outcomes involves a great deal of insight into the particular area one is dealing with, and a considerable amount of intuition about the factors that bear on such outcomes and performances. The…
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…
Inductions and game semantics are two useful extensions to traditional logic programming. To be specific, inductions can capture a wider class of provable formulas in logic programming. Adopting game semantics can make logic programming…
The problem of giving a computational meaning to classical reasoning lies at the heart of logic. This article surveys three famous solutions to this problem - the epsilon calculus, modified realizability and the dialectica interpretation -…
We study how to infer new choices from prior choices using the framework of choice functions, a unifying mathematical framework for decision-making based on sets of preference orders. In particular, we define the natural (most conservative)…
This article is devoted to the tactical game theoretical interpretation of dialectics. Dialectical games are considered as abstractly as well as models of the internal dialogue and reflection. The models related to the representation theory…
Mathematical theorems are human knowledge able to be accumulated in the form of symbolic representation, and proving theorems has been considered intelligent behavior. Based on the BHK interpretation and the Curry-Howard isomorphism, proof…
State of the art machine learning algorithms are highly optimized to provide the optimal prediction possible, naturally resulting in complex models. While these models often outperform simpler more interpretable models by order of…
We offer a view of mathematics as an experimental science where axioms play the role of foundational theories like general relativity and quantum mechanics in physics. Under this view, axioms are provisional and inferred from experience…
Classical probability theory is formulated using sets. In this paper, we extend classical probability theory with propositional computability logic. Unlike other formalisms, computability logic is built on the notion of events/games, which…
We describe several views of the semantics of a simple programming language as formal documents in the calculus of inductive constructions that can be verified by the Coq proof system. Covered aspects are natural semantics, denotational…
We look at intensionality from the perspective of computation. In particular, we review how game semantics has been used to characterize the sequential functional processes, leading to powerful and flexible methods for constructing fully…
Proofs, in Ludics, have an interpretation provided by their counter-proofs, that is the objects they interact with. We follow the same idea by proposing that sentence meanings are given by the counter-meanings they are opposed to in a…