Cycle: XXXVII

PhD student: Nicolò Zamperlin

Role: R1 - First Stage Researcher

Supervisor: Prof. Francesco Paoli

I completed my bachelor and master degrees in Philosophy at the University of Padua, the former one under the supervision of Prof. Carlo Scilironi, the latter one under Prof. Massimiliano Carrara. I also graduated in Logic at the Institute for Logic, Language and Computation of the University of Amsterdam, under the joint supervision of Prof. Robert van Rooij and Prof. Massimiliano Carrara. In both my master theses I studied formal semantics for vague statements. The main areas of my research interest are philosophy of language and formal logic, in particular algebraic logic, which I am currently studying under the supervision of Prof. Francesco Paoli.

THESIS' ABSTRACT

My research project is focused on different kinds of formal systems which can be considered, under different respects, logics of content inclusion, and their interaction with modal operators. In particular I consider the algebraic properties of these logics within the framework of abstract algebraic logic. I have worked mainly on two case studies: containment logics and weak Kleene logics.

Containment logics have their most famous example in Parry's logic of analytic implication ([7]). Starting from recent works on hyperintensionality by Thomas Ferguson ([6]), I provided an alternative semantics for Parry and Ferguson's logics by developing a framework inspired by Richard Epstein's set-assignment semantics ([5]). This generalized Epstein semantics is presented as a flexible tool which can be employed to study many intensional and hyperintensional phenomena, in this special case inclusion of content between premise and conclusion of an implication.

On the second case study there are of weak Kleene logics, the three-valued systems in the Kleene family characterizated by an infective truth value. These system have a nice syntactic characterization in terms of variable inclusion logics ([2]). I have explored the so-called external versions of Bochvar ([1]) and Halldén's ([4]) nonsense logics, which are expressed in a richer language containing classical recapture operators. These logics have an interesting structure theory ([3]) and, unlike their non-external counterparts, they have a well-behaved implication that allows to obtain a meaningful connection with their algebraic semantics. I studied the modal logics built upon weak Kleene external logics and I investigated the classes of algebras which are their algebraic counterparts.

Bibliography

[1] D. Bochvar. On a three-valued logical calculus and its application to the analysis of the paradoxes of the classical extended functional calculus. History and Philosophy of Logic, 2(1-2):87–112, 1981. Translation of the original in Russian (Mathematicheskii Sbornik, 1938).

[2] S. Bonzio, F. Paoli, and M. Pra Baldi. Logics of Variable Inclusion. Springer, Trends in logic, 2022.

[3] S. Bonzio and M. Pra Baldi. On the structure of Bochvar algebras. The Review of Symbolic Logic, 2024.

[4] S. Halldén. The Logic of Nonsense. Lundequista Bokhandeln, Uppsala, 1949.

[5] Epstein, R. L. The Semantic Foundations of Logic. Volume 1: Propositional Logics. Springer Science+Business Media, Dordrecht, Dordrecht, 1990.

[6] Ferguson, T. M. Subject-matter and intensional operators I: Conditional-agnostic analytic implication. Philosophical Studies, 180(7):1849–1879,  2023.

[7] Parry, W. T. Ein axiomensystem für eine neue art von implikation (analytische implikation). Ergebnisse Eines Mathematischen Kolloquiums, 4:5–6, 1933.