Talks by Alexandra Pavlova
My research presentation presentation during the Student Session at Nordic Logic Summer School (N... more My research presentation presentation during the Student Session at Nordic Logic Summer School (NLS) 2017.
Poster for ESSLLI Student Session 2017 (Toulouse). In the paper we define a dialogue system for J... more Poster for ESSLLI Student Session 2017 (Toulouse). In the paper we define a dialogue system for Johansson’s minimal logic. We establish a correspondence between minimal dialogues and sequent calculus. A suitable sequent calculus for minimal logic is introduced.
Dialogue Games for Minimal Logic, 2017
The slides for ESSLLI Student Session 2017 (Toulouse). In the paper we define a dialogue system f... more The slides for ESSLLI Student Session 2017 (Toulouse). In the paper we define a dialogue system for Johansson’s minimal logic. We establish a correspondence between minimal dialogues and sequent calculus. A suitable sequent calculus for minimal logic is introduced.
Логико-философские штудии. Том 13, № 2 (2016)
The paper is aimed at analyzing logical features of cognitive presumptions of rational agents stu... more The paper is aimed at analyzing logical features of cognitive presumptions of rational agents studied and modelled in various logical theories, as well as at comparing them
Санкт-Петербургский государственный университет 2 октября 2015 г.
Conference Presentations by Alexandra Pavlova
IPMU 2020 presentation, 2020
We introduce a game for (extended) Gödel logic where the players’ interaction stepwise reduces cl... more We introduce a game for (extended) Gödel logic where the players’ interaction stepwise reduces claims about the relative order of truth degrees of complex formulas to atomic truth comparison claims. Using the concept of disjunctive game states this semantic game is lifted to a provability game, where winning strategies correspond to proofs in a sequents-of-relations calculus.
The development in modal logic and the emergence of multi-agent formal systems created the necess... more The development in modal logic and the emergence of multi-agent formal systems created the necessary prerequisites for a number of new issues including the idea of the diversity of agents. By the variety of agents we understand the logical diversity that results from various attempts to develop formal systems capable of modeling actions, reasoning and behaviour of actual ration agents. The roots of this idea might be found in various attempts to escape idealizations of agents and their capacities, for instance, logical omniscience when agents know all the consequences of their knowledge and beliefs. Logical omniscience is traditionally related to the axiom K(p → q) → (Kp → Kq) (an epistemic variant of K-axiom (p → q) → (p → q)) that is present in any normal modal system. The idea that real agents are limited in their capacities leads to the idea that different agents have unequal capacities and, thus, have different knowledge, beliefs as well as use diverse rules of inference.
Papers by Alexandra Pavlova
Information Processing and Management of Uncertainty in Knowledge-Based Systems, 2020
We introduce a game for (extended) Gödel logic where the players' interaction stepwise reduces cl... more We introduce a game for (extended) Gödel logic where the players' interaction stepwise reduces claims about the relative order of truth degrees of complex formulas to atomic truth comparison claims. Using the concept of disjunctive game states this semantic game is lifted to a provability game, where winning strategies correspond to proofs in a sequents-of-relations calculus. 1 ⊥ denotes falsum and always evaluates to 0. 2 An order of n values in [0, 1] is given here by 0 0x1 1. .. xn n1, where i ∈ {<, ≤, =}.
Logical Investigations, Dec 23, 2019
In the present paper we introduce a variation of Giles's game that captures the semantics of Slan... more In the present paper we introduce a variation of Giles's game that captures the semantics of Slaney and Meyer's Abelian logic. This is a variation of the game earlier proposed for the Lukasiewicz infinitely-valued logic. We discuss two possible interpretations of this game. One of the interpretations involves a reference to different types of agents. We also give a brief description of the Abelian logic which as well corresponds to one of the comparative logics proposed by Casari. By different types of agents, we understand agents with diverse cognitive presumptions and capabilities. This reflects the idea that different agents can be encoded by a game (dialogue) semantics and truth (and validity) can be seen as a product of different types of communications between agents, establishing the relation between various types of moves available to the players and the resulting type of rationality. However, the main focus of the paper is concentrated on the technical result concerning the game proposed in the paper. In a separate section, we prove that this game is adequate to the Abelian logic. The game can be extended to the one allowing for the disjunctive strategies. As immediate future research, we suggest proving that Proponent's winning strategies for some formula F in the game for Abelian logic A with disjunctive strategies correspond to a derivation of the formula F in the hypersequent calculus GA.
Logical Investigations, 2015
В данной статье рассматривается истинность в том виде, в котором она задается в диалоговой логике... more В данной статье рассматривается истинность в том виде, в котором она задается в диалоговой логике Пауля Лоренцена и Куно Лоренца и в теоретико-игровой семантике (GTS), предложенной Яакко Хинтиккой и разрабатываемой Габриелем Санду. В ходе рассмотрения выявляются и сравниваются основные характеристики семантических концепций, присущих теоретико-игровому подходу (GTS) и диалоговой логике. Таким образом, в статье рассматриваются две концепции истинности, а именно: истинность в теоретико игровой семантике (GTS) и в диалоговой логике. Истинность формулы в обоих подходах определяется как наличие выигрышной стратегии для игрока, отстаивающего данную формулу. Связь между ними заключается в возможности преобразования выигрышной стратегии для игроков в рамках одной системы в выигрышную стратегию для соответствующих игроков в другой посредством строго определенного и конечного алгоритма. Результат данного сравнения позволяет получить определенное представление об отношении между теоретикомодел...
Logic and Logical Philosophy, 2020
In this paper, we define a class of dialogue games for Johansson's minimal logic and prove that i... more In this paper, we define a class of dialogue games for Johansson's minimal logic and prove that it corresponds to the validity of minimal logic. Many authors have stated similar results for intuitionistic and classical logic either with or without actually proving the correspondence. Rahman, Clerbout and Keiff [17] have already specified dialogues for minimal logic; however, they transformed it into Fitch-style natural deduction only. We propose a different specification for minimal logic with the proof of correspondence between the existence of winning strategies for the Proponent in this class of games and the sequent calculus for minimal logic.
Studia Logica
We present a semantic game for Gödel logic and its extensions, where the players’ interaction ste... more We present a semantic game for Gödel logic and its extensions, where the players’ interaction stepwise reduces arbitrary claims about the relative order of truth degrees of complex formulas to atomic ones. The paper builds on a previously developed game for Gödel logic with projection operator in Fermüller et al. (in: M.-J. Lesot, S. Vieira, M.Z. Reformat, J.P. Carvalho, A. Wilbik, B. Bouchon-Meunier, and R.R. Yager, (eds.), Information processing and management of uncertainty in knowledge-based systems, Springer, Cham, 2020, pp. 257–270). This game is extended to cover Gödel logic with involutive negations and constants, and then lifted to a provability game using the concept of disjunctive strategies. Winning strategies in the provability game, with and without constants and involutive negations, turn out to correspond to analytic proofs in a version of $$\text{ SeqGZL } $$ SeqGZL (A. Ciabattoni, and T. Vetterlein, Fuzzy Sets and Systems 161(14):1941–1958, 2010) and in a sequent-o...
We introduce a game for (extended) Gödel logic where the players’ interaction stepwise reduces cl... more We introduce a game for (extended) Gödel logic where the players’ interaction stepwise reduces claims about the relative order of truth degrees of complex formulas to atomic truth comparison claims. Using the concept of disjunctive game states this semantic game is lifted to a provability game, where winning strategies correspond to proofs in a sequents-of-relations calculus.
Logic and Logical Philosophy, 2020
In this paper, we define a class of dialogue games for Johans-son's minimal logic and prove that ... more In this paper, we define a class of dialogue games for Johans-son's minimal logic and prove that it corresponds to the validity of minimal logic. Many authors have stated similar results for intuitionistic and classical logic either with or without actually proving the correspondence. Rah-man, Clerbout and Keiff [17] have already specified dialogues for minimal logic; however, they transformed it into Fitch-style natural deduction only. We propose a different specification for minimal logic with the proof of correspondence between the existence of winning strategies for the Proponent in this class of games and the sequent calculus for minimal logic.
In the present paper we introduce a variation of Giles's game that captures the semantics of Slan... more In the present paper we introduce a variation of Giles's game that captures the semantics of Slaney and Meyer's Abelian logic. This is a variation of the game earlier proposed for the Lukasiewicz infinitely-valued logic. We discuss two possible interpretations of this game. One of the interpretations involves a reference to different types of agents. We also give a brief description of the Abelian logic which as well corresponds to one of the comparative logics proposed by Casari. By different types of agents, we understand agents with diverse cognitive presumptions and capabilities. This reflects the idea that different agents can be encoded by a game (dialogue) semantics and truth (and validity) can be seen as a product of different types of communications between agents, establishing the relation between various types of moves available to the players and the resulting type of rationality. However, the main focus of the paper is concentrated on the technical result concerning the game proposed in the paper. In a separate section, we prove that this game is adequate to the Abelian logic. The game can be extended to the one allowing for the disjunctive strategies. As immediate future research, we suggest proving that Proponent's winning strategies for some formula F in the game for Abelian logic A with disjunctive strategies correspond to a derivation of the formula F in the hypersequent calculus GA.
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Talks by Alexandra Pavlova
Conference Presentations by Alexandra Pavlova
Papers by Alexandra Pavlova