Autumn Semester HS2021

Unless stated otherwise, all talks will take place in room A97 of the Exakte Wissenschaft Building (ExWi) at the University of Bern. Please note that the university requires all seminar attendees have a Covid certificate and to wear a mask.

Schedule

Date Time Speaker Title
30.09.2021 13.30 - 14.15 Atefeh Rohani - University of Bern Explicit non-normal modal logic
07.10.2021 13:00 - 14:00 Gavin St. John - University of Cagliari, Italy Sequent calculi for quantum logic and related structures
14.10.2021 13:00 - 14:00 Line van den Berg - University Grenoble Alpes, France Cultural knowledge evolution in Dynamic Epistemic Logic
28.10.2021 13:00 - 14:00 Simon Santschi - University of Bern
18.11.2021 13.00 - 14.00 Alessandro Facchini The logic of desirability: fundamentals, applications and some problems

Abstracts

Explicit non-normal modal logic

Atefeh Rohani

Faroldi argues that deontic modals are hyperintensional and thus traditional modal logic cannot provide an appropriate formalization of deontic situations. To overcome this issue, we introduce novel justification logics as hyperintensional analogues to non-normal modal logics. We establish soundness and completness with respect to various models and we study the problem of realization.

Sequent calculi for quantum logic and related structures

Gavin St. John

The story of (orthomodular) quantum logic, as motivated by the work of Birkoff and von Neumann, has been a story of varied success. It is well known that the observables of a quantum system can be modeled by complex separable Hilbert space, where the lattice of projection operators upon it form the canonical example of what is known as an orthomodular lattice. Orthomodular lattices form a variety denoted OML.

While the 1-assertional logic of OML is regularly algebraizable with the variety of OML's, many questions have remained famously open; such as decidability of the provability (or even the deducibility) relation. Some sequent calculi have been proposed in the literature (cf. Nishimura 1980, Cutland & Gibbons 1982), however such calculi have not been shown to be (Gentzen-)algebraizable with OML, and have not proved fruitful in answering these questions. Likewise, these issues are mirrored algebraically in OML; it remains unknown whether the equational theory of OML is decidable (or even the word problem), or whether OML admits any form of completions.

Recent attempts have been made to approach these problems under the umbrella of residuated structures, structures which have had great success in answering classical problems in many nonclassical logics. While no (term-definable) operation in OML satisfies the (two-sided) law of residuation, it has been folklore that the Sasaki operations form a one-sided residuated pair; moreover, OML is term definable with the variety OG of orthomodular groupoids (Chajda & Länger 2017). Such structures form a subvariety in the variety PLRG of pointed left-residuated lattice order groupoids (introduced in Fazio, Ledda, & Paoli 2021), perhaps the first "algebraic-umbrella" containing both quantum structures and residuated lattices.

In this talk we will present and motivate an algebraizable sequent calculus whose equivalent algebraic semantics is PLRG, following the traditional "substructural" roadmap (e.g., as in Galatos & Ono 2010). Within this framework, we also present an algebraizable calculus whose equivalent algebraic semantics is OG; realizing orthomodular quantum logic via structural rules. We also discuss the difficulties that naturally arise, and perhaps, are inherent-to such an approach. While we cannot provide any definitive answers to the classical problems, such a marriage of substructural and quantum logics seems fruitful. This is ongoing work in collaboration with Davide Fazio, Antonio Ledda, and Francesco Paoli at the University of Cagliari.

Cultural knowledge evolution in Dynamic Epistemic Logic

Line van den Berg

Agents may use their own, distinct vocabularies to reason and talk about the world, structured into knowledge representations, also called ontologies. In order to communicate, they use alignments: translations between terms of their ontologies. However, ontologies may be subjected to change, when agents learn new terms from their environment or from their peers, requiring their alignments to evolve accordingly. Experimental cultural knowledge evolution aims at studying the mechanisms that agents use to evolve their knowledge and has been applied to the evolution of alignments in the Alignment Repair Game (ARG). Experiments have shown that, through ARG, agents improve their alignments and reach successful communication. Yet, they are not sufficient to understand the formal properties of cultural knowledge evolution.

In this talk, I will present a modeling of ARG in Dynamic Epistemic Logic to assess its formal properties. I will show that all but one adaptation operator are correct, they are incomplete and partially redundant. These properties are, of course, of the game and of the modeling. I will discuss the differences between the two, which inspires to introduce an independent model of awareness based on partial valuations and weakly reflexive relations. This is used to define an alternative modeling of ARG under which the formal properties are re-examined, therefore showing that DEL is insufficient to model cultural knowledge evolution.