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We present syntactic characterisations for the union closed fragments of existential second-order logic and of logics with team semantics. Since union closure is a semantical and undecidable property, the normal form we introduce enables…
As a contribution to the challenge of building game-playing AI systems, we develop and analyse a formal language for representing and reasoning about strategies. Our logical language builds on the existing general Game Description Language…
We study combinatorial games under mis\`ere convention. Several sets of games have been considered earlier to better understand the behaviour of mis\`ere games. We here connect several of these sets. In particular, we prove that comparison…
Modelling compositional meaning for sentences using empirical distributional methods has been a challenge for computational linguists. We implement the abstract categorical model of Coecke et al. (arXiv:1003.4394v1 [cs.CL]) using data from…
Simple reference games are of central theoretical and empirical importance in the study of situated language use. Although language provides rich, compositional truth-conditional semantics to facilitate reference, speakers and listeners may…
In programming language semantics, it has proved to be fruitful to analyze context-dependent notions of computation, e.g., dataflow computation and attribute grammars, using comonads. We explore the viability and value of similar modeling…
We propose a new version of formula size game for modal logic. The game characterizes the equivalence of pointed Kripke-models up to formulas of given numbers of modal operators and binary connectives. Our game is similar to the well-known…
Concept Bottleneck Models (CBMs) provide a basis for semantic abstractions within a neural network architecture. Such models have primarily been seen through the lens of interpretability so far, wherein they offer transparency by inferring…
We introduce operational semantics into games. And based on the operational semantics, we establish a full algebra of games, including basic algebra of games, algebra of concurrent games, recursion and abstraction. The algebra can be used…
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…
Formal argumentation is being used increasingly in artificial intelligence as an effective and understandable way to model potentially conflicting pieces of information, called arguments, and identify so-called acceptable arguments…
In the following paper we present a new semantics for the well-known strategic logic ATL. It is based on adding roles to concurrent game structures, that is at every state, each agent belongs to exactly one role, and the role specifies what…
In this paper we provide a unifying description of different types of semantics of modal logic found in the literature via the framework of topological categories. In the style of categorical logic, we establish an exact correspondence…
We introduce a generalization of the bisimulation game that finds distinguishing Hennessy-Milner logic formulas from every finitary, subformula-closed language in van Glabbeek's linear-time--branching-time spectrum between two finite-state…
Pursuing a new approach to the study of infinite games in combinatorics, we introduce the categories $\mathbf{Game}_{A}$ and $\mathbf{Game}_{B}$ and improve some classical results concerning topological games related to the duality between…
Categorization, a core cognitive ability in humans that organizes objects based on common features, is essential to cognitive science as well as computer vision. To evaluate the categorization ability of visual AI models, various proxy…
While the situation has improved for text-only models, it again seems to be the case currently that multimodal (text and image) models develop faster than ways to evaluate them. In this paper, we bring a recently developed evaluation…
Estimating discrete games of complete information is often computationally difficult due to partial identification and the absence of closed-form moment characterizations. This paper proposes computationally tractable approaches to…
We propose a modal study of the notion of bisimulation. Our contribution is threefold. First, we extend the basic modal language with a new modality $\nbi$, whose intended meaning is universal quantification over all states that are…
An old dream of concurrency theory and programming language semantics has been to uncover the fundamental synchronization mechanisms which regulate situations as different as game semantics for higher-order programs, and Hoare logic for…