Free Logic and the Quantified Argument Calculus

Peer reviewe

Neutral Free Logic: Motivation, Proof Theory and Models

Free logics are a family of first-order logics which came about as a result of examining the existence assumptions of classical logic (Hintikka The Journal of Philosophy, 56, 125-137 1959;Lambert Notre Dame Journal of Formal Logic, 8, 133-144 1967, 1997, 2001). What those assumptions are varies, but the central ones are that (i) the domain of interpretation is not empty, (ii) every name denotes exactly one object in the domain and (iii) the quantifiers have existential import. Free logics reject the claim that names need to denote in (ii). Positive free logic concedes that some atomic formulas containing non-denoting names (including self-identity) are true, negative free logic treats them as uniformly false, and neutral free logic as taking a third value. There has been a renewed interest in analyzing proof theory of free logic in recent years, based on intuitionistic logic in Maffezioli and Orlandelli (Bulletin of the Section of Logic, 48(2), 137-158 2019) as well as classical logic in Pavlovi and Gratzl (Journal of Philosophical Logic, 50, 117-148 2021), there for the positive and negative variants. While the latter streamlines the presentation of free logics and offers a more unified approach to the variants under consideration, it does not cover neutral free logic, since there is some lack of both clear formal intuitions on the semantic status of formulas with empty names, as well as a satisfying account of the conditional in this context. We discuss extending the results to this third major variant of free logics. We present a series of G3 sequent calculi adapted from Fjellstad (Studia Logica, 105(1), 93-119 2017, Journal of Applied Non-Classical Logics, 30(3), 272-289 2020), which possess all the desired structural properties of a good proof system, including admissibility of contraction and all versions of the cut rule. At the same time, we maintain the unified approach to free logics and moreover argue that greater clarity of intuitions is achieved once neutral free logic is conceptualized as consisting of two sub-varieties

Proof-Theoretic Analysis of the Logics of Agency. : The Deliberative STIT

A sequent calculus methodology for systems of agency based on branching-time frames with agents and choices is proposed, starting with a complete and cut-free system for multi-agent deliberative STIT; the methodology allows a transparent justification of the rules, good structural properties, analyticity, direct completeness and decidability proofs.Peer reviewe

TGF-β-Id1 Signaling Opposes Twist1 and Promotes Metastatic Colonization via a Mesenchymal-to-Epithelial Transition

ID genes are required for breast cancer colonization of the lungs, but the mechanism remains poorly understood. Here, we show that Id1 expression induces a stem-like phenotype in breast cancer cells while retaining epithelial properties, contrary to the notion that cancer stem-like properties are inextricably linked to the mesenchymal state. During metastatic colonization, Id1 induces a mesenchymal-to-epithelial transition (MET), specifically in cells whose mesenchymal state is dependent on the Id1 target protein Twist1, but not at the primary site, where this state is controlled by the zinc finger protein Snail1. Knockdown of Id expression in metastasizing cells prevents MET and dramatically reduces lung colonization. Furthermore, Id1 is induced by transforming growth factor (TGF)-β only in cells that have first undergone epithelial-to-mesenchymal transition (EMT), demonstrating that EMT is a prerequisite for subsequent Id1-induced MET during lung colonization. Collectively, these studies underscore the importance of Id-mediated phenotypic switching during distinct stages of breast cancer metastasis