相关论文: Second-Order Type Isomorphisms Through Game Semant…
We discuss quantitative Calder\'on-Zygmund estimates in $W^{2,2}$ for 2D viscous Hamilton-Jacobi equations with natural growth in the gradient. We apply the result to obtain the existence of classical solutions for stationary second order…
Expansion of the categorical point of view on many areas of the mathematics and mathematical physics will cause to deeper understanding of genuine features of these problems. New applications of categorical methods are connected with new…
This paper contains a study of multivariate second order stochastic mappings indexed by an abstract set $\Lambda$ in close connection to their operator covariance functions. The characterizations of the normal Hilbert module or of Hilbert…
Mental representation, characterized by structured internal models mirroring external environments, is fundamental to advanced cognition but remains challenging to investigate empirically. Existing theory hypothesizes that second-order…
Second-order superintegrable systems in dimensions two and three are essentially classified. With increasing dimension, however, the non-linear partial differential equations employed in current methods become unmanageable. Here we propose…
We review the close relationship between abstract machines for (call-by-name or call-by-value) lambda-calculi (extended with Felleisen's C) and sequent calculus, reintroducing on the way Curien-Herbelin's syntactic kit expressing the…
2-Theories are a canonical way of describing categories with extra structure. 2-theory-morphisms are used when discussing how one structure can be replaced with another structure. This is central to categorical coherence theory. We place a…
Generalizing standard monadic second-order logic for Kripke models, we introduce monadic second-order logic interpreted over coalgebras for an arbitrary set functor. We then consider invariance under behavioral equivalence of MSO-formulas.…
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 introduce the countdown $\mu$-calculus, an extension of the modal $\mu$-calculus with ordinal approximations of fixpoint operators. In addition to properties definable in the classical calculus, it can express (un)boundedness properties…
Much work has been done to give semantics to probabilistic programming languages. In recent years, most of the semantics used to reason about probabilistic programs fall in two categories: semantics based on Markov kernels and semantics…
We present an algorithm for deriving a spatial-behavioral type system from a formal presentation of a computational calculus. Given a 2-monad Calc: Catv$\to$ Cat for the free calculus on a category of terms and rewrites and a 2-monad…
The game-theoretic risk management framework put forth in the precursor work "Towards a Theory of Games with Payoffs that are Probability-Distributions" (arXiv:1506.07368 [q-fin.EC]) is herein extended by algorithmic details on how to…
We develop the theory of strong and commutative monads in the 2-dimensional setting of bicategories. This provides a framework for the analysis of effects in many recent models which form bicategories and not categories, such as those based…
Isomorphism is central to the structure of mathematics and has been formalized in various ways within dependent type theory. All previous treatments have done this by replacing quantification over sets with quantification over groupoids of…
In the $(G,H)$-isomorphism game, a verifier interacts with two non-communicating players (called provers) by privately sending each of them a random vertex from either $G$ or $H$, whose aim is to convince the verifier that two graphs $G$…
We develop a second-order extension of intuitionistic modal logic, allowing quantification over propositions, both syntactically and semantically. A key feature of second-order logic is its capacity to define positive connectives from the…
Our purpose is to focus attention on a new criterion for quantum schemes by bringing together the notions of quantum game and game isomorphism. A quantum game scheme is required to generate the classical game as a special case. Now, given a…
The aim of this paper is to bring together the notions of quantum game and game isomorphism. The work is intended as an attempt to introduce a new criterion for quantum game schemes. The generally accepted requirement forces a quantum…
The present paper gives a mathematical, in particular, syntax-independent, formulation of intensionality and dynamics of computation in terms of games and strategies. Specifically, we give a game semantics for a higher-order programming…