Related papers: Games for Dependent Types
Classify simple games into sixteen "types" in terms of the four conventional axioms: monotonicity, properness, strongness, and nonweakness. Further classify them into sixty-four classes in terms of finiteness (existence of a finite carrier)…
We introduce some new logics of imperfect information by adding atomic formulas corresponding to inclusion and exclusion dependencies to the language of first order logic. The properties of these logics and their relationships with other…
Axioms are presented which encapsulate the properties satisfied by categories of games which form the basis of results on full abstraction for PCF and other programming languages, and on full completeness for various logics and type…
Agda is a dependently-typed programming language and a proof assistant, pivotal in proof formalization and programming language theory. This paper extends the Agda ecosystem into machine learning territory, and, vice versa, makes…
Cross-language authorship attribution problems rely on either translation to enable the use of single-language features, or language-independent feature extraction methods. Until recently, the lack of datasets for this problem hindered the…
In this paper we propose a categorical theory of intensionality. We first revisit the notion of intensionality, and discuss we its relevance to logic and computer science. It turns out that 1-category theory is not the most appropriate…
To be usable in practice, interactive theorem provers need to provide convenient and efficient means of writing expressions, definitions, and proofs. This involves inferring information that is often left implicit in an ordinary…
Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the…
This paper presents a novel method for enhancing the adaptability of Proportional-Integral-Derivative (PID) controllers in industrial systems using event-based dynamic game theory, which enables the PID controllers to self-learn, optimize,…
A recently proposed axiom system for Andr\'e's central translation structures is improved upon. First, one of its axioms turns out to be dependent (derivable from the other axioms). Without this axiom, the axiom system is indeed…
The usual homogeneous form of equality type in Martin-L\"of Type Theory contains identifications between elements of the same type. By contrast, the heterogeneous form of equality contains identifications between elements of possibly…
This work introduces the concept of Variable Size Game Theory (VSGT), in which the number of players in a game is a strategic decision made by the players themselves. We start by discussing the main examples in game theory: dominance,…
We introduce the Delta-framework, LF-Delta, a dependent type theory based on the Edinburgh Logical Framework LF, extended with the strong proof-functional connectives, i.e. strong intersection, minimal relevant implication and strong union.…
We develop the theory of generically stable types, independence relation based on nonforking and stable weight in the context of dependent (NIP) theories.
We try to understand complete types over a somewhat saturated model of a complete first order theory which is dependent (previously called NIP), by "decomposition theorems for such types". Our thesis is that the picture of dependent theory…
We show that the classifying category C(T) of a dependent type theory T with axioms for identity types admits a non-trivial weak factorisation system. We provide an explicit characterisation of the elements of both the left class and the…
We construct a model of strategic imitation in an arbitrary network of players who interact through an additive game. Assuming a discrete time update, we show a condition under which the resulting difference equations converge to consensus.…
Autonomous agents powered by large language models (LLMs) enable novel use cases in domains where responsible action is increasingly important. Yet the inherent unpredictability of LLMs raises safety concerns about agent reliability. In…
Dependently typed languages are well known for having a problem with code reuse. Traditional non-indexed algebraic datatypes (e.g. lists) appear alongside a plethora of indexed variations (e.g. vectors). Functions are often rewritten for…
We describe a type system for a platform called the General Intensional Programming System (GIPSY), designed to support intensional programming languages built upon intensional logic and their imperative counter-parts for the intensional…