neighborhood semantics

This study addresses the limitations of traditional action logics in capturing how agents determine outcomes through their actions. It proposes InqAL, a multi-agent modal logic that integrates inquisitive logic with action efficacy for the first time, formalizing the notion of “agent determinacy” within concurrent game structures. By employing an inquisitive neighborhood semantics, a sound and complete axiomatization, and a representation theorem, the framework precisely characterizes realizable effectivity functions. The work establishes the completeness of InqAL’s axiom system, proves that the logic enjoys the finite model property and is decidable, and provides necessary and sufficient conditions for neighborhood frames to originate from concurrent game structures.

This work bridges the theoretical gap between concurrent game semantics (dynamic models) and compositional structural semantics (static models). We introduce the first oplax functor from the category of thin concurrent event structures to the category of generalized structural species, modeling strategies as distributors equipped with visibility and payoff structure, and construct a compact semantic bridge preserving linear structure and resource symmetries. This mapping is further lifted to a Cartesian closed pseudofunctor, thereby unifying, at the bicategorical level, the functional behavior of λ-calculus with concurrent interaction. The resulting framework provides the first bicategorical unification for linear logic, resource-sensitive computation, and functional programming semantics—simultaneously supporting dynamic game-theoretic interpretation and static compositional expressivity.

Existing semantic frameworks for asynchronous multi-agent systems (MAS) inaccurately assess strategic capability—overlooking finite paths and deadlocks, and failing to capture the asymmetry between active agents and passive objects. Method: We reconstruct execution semantics and state representation, proposing an extended strategic logic semantic framework. Specifically, we formally model strategic deadlocks and agent–object asymmetry in asynchronous MAS for the first time, and design a revised execution model compatible with model reduction. Contributions: (1) We eliminate counterintuitive evaluations of strategic formulas, yielding semantics that faithfully reflect real-world asynchronous interactions; (2) We rigorously prove that classical model reduction algorithms remain sound and complete under the new semantics; (3) We establish a novel foundation for distributed strategy verification based on ATL/STIT, balancing expressive power with computational tractability. This framework enables precise, scalable reasoning about strategic abilities in asynchronous, decentralized settings.

Tsukada and Ong established an indirect proof of the correspondence between simple typed normal η-long resource terms and Hyland–Ong game semantics, lacking a direct, constructive semantic account. Method: We introduce *augmentations* as canonical causal structures to model resource terms and their β-reduction dynamics up to homotopy equivalence; based on this, we define weighted strategies and construct a denotational model that preserves reduction. Contribution/Results: First, we establish an explicit syntactic–semantic correspondence for resource terms grounded directly in augmentations. Second, we propose the *resource category*, a novel categorical framework providing an axiomatized semantic foundation for resource calculi—paralleling how differential categories underpin differential λ-calculi. Third, our approach eliminates reliance on relational models, enabling intrinsic, dynamic modeling of reduction processes within the semantics itself. This yields a fully compositional, reduction-respecting interpretation of resource computation.

This paper addresses the ambiguous boundary between “strategic” and “non-strategic” behavior in behavioral game theory—particularly the lack of a rigorous, formal definition of non-strategic behavior under bounded rationality. To resolve this, we introduce the first axiomatic characterization of non-strategic behavior: actions that do not model others’ beliefs or decision processes. Our definition subsumes all canonical non-strategic rules in the literature—including Nash indifference, level-0 reasoning in cognitive hierarchy models, and reactive heuristics—and is provably disjoint from any strategic behavior in a mathematically precise sense. Methodologically, we integrate tools from game theory, formal logic, and decision theory, constructing an axiom system and establishing separation via model-theoretic proofs. The resulting framework provides the first universally applicable and decidable formal foundation for modeling bounded rationality, designing multi-agent systems, and advancing cognitive hierarchy theory.

This study addresses the axiomatization of multimodal logics induced by three natural neighborhood functions within the framework of full product neighborhoods, focusing on the frame classes validating the modal logics T and D. By combining three monomodal logics and introducing an interaction axiom (mix), the authors construct the trimodal logics Tx+T and Dx+D. The work innovatively extends known product logic results for S4 and D4 to the weaker systems T and D, revealing that the role of (mix) varies across logical contexts: in S4, (mix) is equivalent to (sub), thereby enabling an axiomatization of the full product logic over topological spaces. The main contributions establish that Tx+T equals the product logic T×T×T augmented with (mix), and similarly, Dx+D equals D×D×D plus (mix).

This work establishes a fully abstract correspondence between base-extension semantics (B-eS) in proof-theoretic semantics and Hyland–Ong game semantics, aiming to unify intensional accounts of meaning for logical systems. By linking the dynamic, interactive nature of logical inference with atom-based provability, the study develops an intensional semantic framework grounded in proof computation and integrates Sandqvist-style completeness techniques. It presents the first fully abstract connection between B-eS and Hyland–Ong game semantics, yielding a sound and complete semantic characterization for intuitionistic propositional logic. The expressiveness and applicability of the framework are further demonstrated through a case study on a 4×4 Sudoku puzzle.

This study investigates the representation of effective and α-power for coalitions within generalized concurrent game frameworks that abandon the assumption of agent independence. By deconstructing structural assumptions of standard concurrent games—such as sequentiality, determinism, and agent independence—the authors construct eight generalized frameworks and focus on four classes where agent independence does not hold. Integrating modal logic semantics, neighborhood semantics, and game-theoretic reasoning, they employ structural decomposition and bisimulation techniques to establish, for the first time, complete representation theorems mapping these two notions of power onto corresponding neighborhood frames. This work extends the semantic foundations of strategic reasoning logics and provides novel formal tools for reasoning about environments with interdependent agents.

This work addresses the lack of quantitative semantics and the difficulty in expressing neighborhood counting constraints in Signal Temporal Logic with Graph Operators (STL-GO) by proposing the first quantitative semantic framework. The approach employs a layered algebraic construction that decouples temporal reasoning from graph-operator aggregation, introducing an abstract accumulator equipped with monotonic folding and readout mechanisms. Logical soundness and completeness are reduced to monotonicity conditions on the accumulator. The framework supports multiple semantic instantiations and is validated on both a two-dimensional Dubins car scenario and a three-dimensional Earth-satellite system, demonstrating Boolean, extremal, signed-deficit, and hybrid semantics. These experiments reveal inherent trade-offs between scalability and expressiveness across different accumulator designs.

This work addresses the challenge of coordinating heterogeneous autonomous agents in dynamic adversarial environments, where geometric constraints, logical consistency, temporal reasoning, and strategic optimization must be jointly satisfied. Existing topological and sheaf-theoretic approaches struggle to explicitly model value and strategy selection. To overcome this limitation, the paper proposes a unified categorical framework that embeds event calculus, SCEL-based coalition formation, and game-theoretic reward structures into a Grothendieck topos. Within this setting, utility functions and strategy distributions are modeled via a novel “game sheaf,” while restriction maps capture parallel transport and best-response dynamics. The key contributions include proving that Nash equilibria correspond to global sections of the best-response sheaf, employing cohomological obstructions to classify failures of strategic consistency, and, for the first time, integrating strategic rationality with multi-agent coordination within sheaf theory. The framework’s expressive power is validated through an immunological “fortress defense” scenario, demonstrating its capacity to represent self-organized, equilibrium strategies under resource constraints, thereby laying a theoretical foundation for verifiable, autonomous, and economically rational multi-agent systems.