Related papers: Convergence, Continuity and Recurrence in Dynamic …
One of the highlights of recent informal epistemology is its growing theoretical emphasis upon various notions of context. The present paper addresses the connections between knowledge and context within a formal approach. To this end, a…
We study conflict situations that dynamically arise in traffic scenarios, where different agents try to achieve their set of goals and have to decide on what to do based on their local perception. We distinguish several types of conflicts…
This paper investigates spaces equipped with a family of metric-like functions satisfying certain axioms. These functions provide a unified framework for defining topology, uniformity, and diffeology. The framework is based on a family of…
Evaluating the quality of reasoning traces from large language models remains understudied, labor-intensive, and unreliable: current practice relies on expert rubrics, manual annotation, and slow pairwise judgments. Automated efforts are…
The behavior of complex systems is determined not only by the topological organization of their interconnections but also by the dynamical processes taking place among their constituents. A faithful modeling of the dynamics is essential…
Computational topology has recently known an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this field.…
In the present paper, we introduce a multi-type display calculus for dynamic epistemic logic, which we refer to as Dynamic Calculus. The display-approach is suitable to modularly chart the space of dynamic epistemic logics on…
We propose a number of powerful dynamic-epistemic logics for multi-agent information sharing and acts of publicly or privately accessing other agents' information databases. The static base of our logics is obtained by adding to standard…
The main result of this paper is a proof using real analysis of the monotonicity of the topological entropy for the family of quadratic maps, sometimes called Milnor's Monotonicity Conjecture. In contrast, the existing proofs rely in one…
This review presents recent and older results on elementary quantitative and qualitative aspects of consciousness and cognition and tackles the question "What is consciousness?" conjointly from biological, neuroscience-cognitive, physical…
While probability theory is normally applied to external environments, there has been some recent interest in probabilistic modeling of the outputs of computations that are too expensive to run. Since mathematical logic is a powerful tool…
Substantial efforts have been made in developing various Decision Modeling formalisms, both from industry and academia. A challenging problem is that of expressing decision knowledge in the context of incomplete knowledge. In such contexts,…
This paper studies topological definitions of chain recurrence and shadowing for continuous endomorphisms of topological groups generalizing the relevant concepts for metric spaces. It is proved that in this case the sets of chain recurrent…
I introduce PEDAL -- a probabilistic epistemic logic meant to capture, in propositional dynamic terms, the epistemic state of an agent engaged in checking whether a program meets its specification. Semantically, PEDAL is built `on top of'…
Efforts to ensure the safe development of artificial general intelligence (AGI) often rely on consensus-based alignment approaches grounded in axiomatic formalism, interpretability, and empirical validation. However, these methods may be…
This paper presents an extension of temporal epistemic logic with operators that quantify over agent strategies. Unlike previous work on alternating temporal epistemic logic, the semantics works with systems whose states explicitly encode…
One of the prime motivation for topology was Homotopy theory, which captures the general idea of a continuous transformation between two entities, which may be spaces or maps. In later decades, an algebraic formulation of topology was…
Applying dynamic logics to program verifications is a challenge, because their axiomatic rules for regular expressions can be difficult to be adapted to different program models. We present a novel dynamic logic, called DLp, which supports…
There is growing interest in termination reasoning for non-linear programs and, meanwhile, recent dynamic strategies have shown they are able to infer invariants for such challenging programs. These advances led us to hypothesize that…
Standard epistemic logics introduce a modal operator K to represent knowledge, but in doing so they presuppose the logical apparatus they aim to explain. By contrast, this paper explores how logic may be derived from the structure of…