Program & Abstracts
Program
Monday November 7, 2022
10:00 -- 11:15 Marcelo Coniglio "On First-Order Ivlev-like Modal Logic"
11:30 -- 12:45 Pawel Pawlowski "8-valued non-deterministic semantics for modal logics: what modal logics can we find there?"
13:45 -- 15:00 Elio La Rosa "Non-deterministic Connectives and Epsilon Modal Logic"
15:15 -- 16:30 Satoru Niki "Revisiting Kearns' semantics for intuitionistic logic"
16:45 -- 18:00 Daniel Skurt "The smallest modal logic and its extensions"
19:30 Workshop Dinner at Bat Viet
Tuesday, November 8, 2022
10:00 -- 11:15 Ekaterina Kubyshkina "On modal translations of many-valued logics." [online]
11:30 -- 12:45 Lukas Grätz "Truth tables for modal logics with non-deterministic semantics"
13:45 -- 15:00 Guilherme Vicentin de Toledo "Restricted Nmatrices and Logics of Incompatibility"
15:15 -- 16:30 Yoni Zohar "Effective Semantics for the Modal Logics K and KT via Non-deterministic Matrices"
Abstracts
Marcelo Coniglio "On First-Order Ivlev-like Modal Logic"
Pawel Pawlowski "8-valued non-deterministic semantics for modal logics: what modal logics can we find there?"
Recently a quasi-extensional or non-deterministic approach to modality is becoming more popular. The main idea behind this approach is to represent modal systems through non-deterministic semantics. These semantics are a generalization of the standard matrix semantics. In non-deterministic semantics, the interpretation of connectives assigns a non-empty set of values to a formula instead of singling out a unique value. Relaxing the interpretation of connectives allows for the natural representation of modes of propositions by using truth values. So, the logical values not only convey information about the truth status of a given claim but also about its possibility/necessity.
In this talk, we'll study a particular non-deterministic family of semantics with eight values constructed by (Omori and Skurt) and (Cognilio et al.). Values in these semantics convey information about a proposition's truth/falsity, whether the proposition is possible/not possible, and whether it is necessary/not necessary. Each such triple is represented by a unique value.
In our talk, we will examine what modal logics we can obtain by changing the interpretation of the $\B$ modality, assuming that the interpretation of other connectives is constant. We show what axioms are responsible for a particular interpretation of box modality. Next, we study the subsets of these axioms.
Elio La Rosa "Non-deterministic Connectives and Epsilon Modal Logic"
In this talk, I sketch some new, work in progress accounts related to the very notion of indeterminacy giving a new characterization to some structures and properties already surfaced in the literature of non-deterministic (modal) logic. The talk is divided in two parts. In the first, I develop a notion of non-deterministic connectives. These are syntactic expressive devices capturing the very idea of indeterminacy in the language. In the second, I develop a new class of modal logic, which I call epsilon modal logic. These make use of another syntactic device capturing the idea of a choice over a set of valuations satisfying a formula, and mimic the behavior of Hilbert's Epsilon Calculus. The two accounts seem to be strongly related to each other, as they both seem to capture some `self-dual' and functional structure.
Satoru Niki "Revisiting Kearns' semantics for intuitionistic logic"
J.T. Kearns (1978,1981) introduced Justification semantics for intuitionistic logic, which is motivated from the criterion of assertibility. The semantics is distinctive in its employment of non-deterministic matrices, but this also leads to a certain level of complexity. In the talk, we discuss a simplification of the semantics in terms of signed forcings, and then discuss an alternative account of constructive disjunction that can be unearthed from the semantics.
Daniel Skurt "The smallest modal logic and its extension"
Ekaterina Kubyshkina "On modal translations of many-valued logics." [online]
In this talk I will discuss some expressivity results for many-valued and modal logics and survey some translations between these two settings. In particular, two possible strategies for defining these translations will be presented: the linear translations, i.e., translations which preserve the length of the formula, and the exponential ones, which do not preserve the structure of the translated formulas. After discussing the advantages and the drawbacks of each strategy, I will introduce an original exponential translation of each four-valued logic into minimal modal logic, interpreted on neighbourhood semantics.
Lukas Grätz "Truth tables for modal logics with non-deterministic semantics"
In will talk about the construction of truth tables for some very simple modal logics. This is based on the recent development in non-deterministic semantics with level evaluations as pioneered by John T. Kearns and Juri V. Ivlev. We will briefly look at an alternative construction by Arnould Bayart. And there will be an excursus on tableau systems.
Guilherme Vicentin de Toledo "Restricted Nmatrices and Logics of Incompatibility"
Yoni Zohar "Effective Semantics for the Modal Logics K and KT via Non-deterministic Matrices"
A four-valued semantics for the modal logic K is introduced. Possible worlds are replaced by a hierarchy of four-valued valuations, where the valuations of the first level correspond to valuations that are legal w.r.t. a basic non-deterministic matrix, and each level further restricts its set of valuations. The semantics is proven to be effective, and to precisely capture derivations in a sequent calculus for K of a certain form. Similar results are then obtained for the modal logic KT, by simply deleting one of the truth values.