Autumn school "Logic and Formal Philosophy 2024"

In terms of the semantics of possible worlds, the sentence "John could be higher than Mary, as she is" attributes the relationship "higher" to John, as he is in some possible world, and Mary, as she is in the real world. This is an example of cross-world predication. Cross-world predication is the attribution of relationships to objects, each of which is associated with some possible world (an object associated with a possible world w is an object, as it is in W.) Cross-world predication cannot be expressed in standard first-order modal logic; its expression requires non-standard logics with special syntactic and/or semantic properties. The course describes three logics of this type (Wehmeyer's subjunctive logic, Kocurek's hybrid logic and the logic developed by the author) and demonstrates their expressive capabilities. (The course is taught in Russian.)

The combination of quantifiers and modalities is an important plot for both analytical metaphysics and pure logic. The course will consider three variants of Kripke semantics for modal predicate logic: semantics with permanent domains, semantics with growing domains and semantics with variable domains.  We will consider Hilbert calculus adequate to these semantics and focus on proving completeness theorems. Let's discuss the role of the famous Barcan formula (scheme) in proofs, as well as the relationship between the three types of semantics. To master the course, it is desirable to have an idea of the proofs of completeness theorems for propositional modal logic and classical predicate logic.  References: Brauner T., Ghilardi S. First-Order Modal Logic // Handbook of Modal Logic. Amsterdam: Elsevier, 2006. P. 549-620; Garson J.W. Quantification in Modal Logic // Handbook of Philosophical Logic Vol. 3.  Amsterdam:  Kluwer, 2001.  P. 267-323;  Gabbay D., Skvortsov D., Shehtman V. Quantification in nonclassical logic. Amsterdam:  Elsevier, 2009. (The course is taught in Russian.)

The interpretations of abstract (model-theoretic) logics as structures and as classifications of structures will be compared, and some plots from the early history of model theory related to the formation of its conceptual apparatus (semantic completeness, categoricity, definite manifold, etc.) will be considered. (The course is taught in Russian.)

The course consists of four parts by content, combined in pairs into two lectures. The first part will be devoted to the basics of situational semantics: its ideology, conceptual apparatus and formal representation of the meaning of a sentence in the form of a relationship between situations. The second part will show how the described approach is applied to the analysis of the meaning of proper names and indexicals. The third part will be devoted to the meaning of certain descriptions in various ways of using them and the conditions of their significance, usually called presuppositions. In the fourth part, we will consider the situation semantics approach to modeling epistemic attitudes, formulate a solution to the Frege's puzzle with proper names from the point of view of this approach and try to compare it with other approaches to this problem. (The course is taught in Russian.)

The course will present an intuitionistic view of knowledge, which, on the one hand, preserves the semantics of Brower-Geiting-Kolmogorov intuitionism, and on the other hand, it is consistent with the well-known approach according to which intuitionistic knowledge should be considered as the result of verification. The first part of the course assumes a meaningful discussion of axioms containing the modality of knowledge and statements added to the intuitionistic logic. In the second part of the course, we will look at Kripke type semantics, prove the completeness theorem, and discuss some related issues. (The course is taught in Russian.)

It is proposed to consider algorithmic issues for first—order logics and theories, both classical and non-classical. Using the domino technique, it is supposed to prove the Church and Trakhtenbrot’s theorems for classical logics and binary predicate theories, and then extract consequences for non-classical (primarily modal) logics of the unary predicate related to the insolubility of their corresponding fragments. In addition, it is intended to discuss the limitations that arise in evidence and show situations where their violation leads to solvable fragments. (The course is taught in Russian.)

This mini-course intends to show the recent developments on non-deterministic semantics for non-classical logics, with emphasis on the paraconsistent logics known as Logics of Formal Inconsistency (LFIs), Logics of Evidence and Truth (LETs) and some Ivlev-like modal logics. The main semantic tools to be considered are non-deterministic matrices (Nmatrices), possibly with restrictions on the valuations (restricted Nmatrices). An analytical way to describe Nmatrices will be given by means of swap structures, which naturally generalize twist structures to the non-deterministic framework. A natural way to combine swap structures by fibring will also be analyzed.

Program:

Lecture #1: Non-deterministic matrices (Nmatrices) and swap structures for Logics of Formal Inconsistency (LFIs), Logics of Evidence and Truth (LETS) and Ivlev-like modal Logics.

Lecture #2: Limitations of Nmatrix semantics: extension to Restricted Nmatrices (RNmatrices). Applications to da Costa's paraconsistent logics and to normal modal logics.

Lecture #3: Combination of swap structures: Fibring of clausal bivalorations and the generated swap structures. Soundness and Completeness preservation results by fibring.

Application: combination of Ivlev-like modal logics with LFIs and LETs.

We discuss how strategic and naive Interactions of agents depend on Kripke structure in terms of Dynamic Epistemic Logic. For example, we use this approach to discuss Cheryl's birthday example, Russian Card games and their new modifications and applications like Secured Communacation Protocol and AI. We also discuss transformation of Kripke structures into Generalized Multiple Awareness Structures as a way to easily find Bayesian-Nash equilibrium.

In this course we will survey the most remarkable logical contributions and theoretical findings in the Western thinking tradition in order to understand how a truly paraconsistent perspective has been constituted, as well as how logical principles, rules and systems could have been expressed various concepts of paraconsistency. In the history of logic, we will trace the answers to some fundamental questions, such as how logical principles and rules were conceived, evoked, or introduced within certain theoretical contexts and traditions. These principles and rules dictate that not everything may be deduced from a contradiction, or that something may be rejected. We will employ advanced historiographical categories to deal with logical contributions to the history of paraconsistent logic, providing a critical assessment of paraconsistent-like positions in ancient Greek logic, medieval scholastic logic, modern logic, and the era of paraconsistent logic systems. In establishing paraconsistent logic, we will emphasize the crucial contributions of Stanislaw Jaskowski (1948) and Newton da Costa (1963), with special attention to the legacy of these fundamental contributions to the further development of paraconsistency as a fruitful field of research. References:  Gomes, E. L., D’Ottaviano, I. M. L. Para além das Colunas de Hércules, uma história da paraconsistência: de Heráclito a Newton da Costa [Beyond the Columns of Hercules, a history of paraconsistency: from Heraclitus to Newton da Costa], in Portuguese). Campinas: Editora Unicamp and Centro de Lógica, Epistemologia e História da Ciência, 2017. (Coleção CLE, 80; Unicamp Ano 50, 50).

I intend to discuss the original and innovative works of Vasiliev, Florensky, Kolmogorov, Orlov and Bochvar. (The course is taught in English.)