The modes of physical properties in the logical foundations of physics

We present a conceptual analysis of the notions of actual physical property and potential physical property as used by theoretical physicists/mathematicians working in the domain of operational quantum logic. We investigate how these notions are being used today and what role they play in the specified field of research. In order to do so, we will give a brief introduction to this area of research and explain it as a part of the discipline known as “mathematical metascience”. An in depth analysis of Aristotle’s use of the notions of “actuality” and “potentiality” is presented in order to point out exactly how much of the Aristotelian connotations are embedded in the contemporary use of the concepts under investigation. Although we will not focus in depth on all the drawbacks in the early historical development of physics due to the overwhelming influence of Aristotle’s writings, our analysis does touch upon some aspects of the Aristotelian theory of movement that are often overthrown nowadays

Argument-based Belief in Topological Structures

This paper combines two studies: a topological semantics for epistemic notions and abstract argumentation theory. In our combined setting, we use a topological semantics to represent the structure of an agent's collection of evidence, and we use argumentation theory to single out the relevant sets of evidence through which a notion of beliefs grounded on arguments is defined. We discuss the formal properties of this newly defined notion, providing also a formal language with a matching modality together with a sound and complete axiom system for it. Despite the fact that our agent can combine her evidence in a 'rational' way (captured via the topological structure), argument-based beliefs are not closed under conjunction. This illustrates the difference between an agent's reasoning abilities (i.e. the way she is able to combine her available evidence) and the closure properties of her beliefs. We use this point to argue for why the failure of closure under conjunction of belief should not bear the burden of the failure of rationality.Comment: In Proceedings TARK 2017, arXiv:1707.0825

Correlated Knowledge:An Epistemic-Logic View on Quantum Entanglement

In this paper we give a logical analysis of both classical and quantum correlations We propose a new logical system to reason about the information carried by a complex system composed of several parts Our formalism is based on an extension of epistemic logic with operators for "group knowledge" (the logic GEL), further extended with atomic sentences describing the results of joint observations" (the logic LCK) As models we introduce correlation models, as a generalization of the standard representation of epistemic models as vector models We give sound and complete axiomatizations for our logics, and we use this setting to investigate the relationship between the information carried by each of the parts of a complex system and the information carried by the whole system In particular we distinguish between the "distributed information", obtainable by simply pooling together all the information that can be separately observed in any of the parts and correlated information, obtainable only by doing joint observations of the parts (and pooling together the results) Our formalism throws a new light on the difference between classical and quantum information and gives rise to an informational-logical characterization of the notion of "quantum entanglement