•  111
    Logic of Change, Change of Logic
    with Hans van Ditmarsch and Brian Hill
    Synthese 171 (2). 2009.
  •  43
    This volume presents mathematical game theory as an interface between logic and philosophy.
  •  36
    In the majority of papers on probability in the framework of possible worlds the existence of a global probability distribution is taken for granted. The aim of the article is to discuss the epistemic aspect of this assumption in the connection to the status assigned to possible worlds. Two questions are discussed in particular: the justification of the global probability distribution and compatibility of the global probability assumption with the structure of the universe of the possible worlds…Read more
  •  34
    Interpreting Probability
    Journal of Logic, Language and Information 21 (2): 141-144. 2012.
  •  29
    Empiricism in the foundations of cognition
    AI and Society 38 (1): 67-87. 2023.
    This paper traces the empiricist program from early debates between nativism and behaviorism within philosophy, through debates about early connectionist approaches within the cognitive sciences, and up to their recent iterations within the domain of deep learning. We demonstrate how current debates on the nature of cognition via deep network architecture echo some of the core issues from the Chomsky/Quine debate and investigate the strength of support offered by these various lines of research …Read more
  •  27
    Probabilities with Gaps and Gluts
    Journal of Philosophical Logic 50 (5): 1107-1141. 2021.
    Belnap-Dunn logic, sometimes also known as First Degree Entailment, is a four-valued propositional logic that complements the classical truth values of True and False with two non-classical truth values Neither and Both. The latter two are to account for the possibility of the available information being incomplete or providing contradictory evidence. In this paper, we present a probabilistic extension of BD that permits agents to have probabilistic beliefs about the truth and falsity of a propo…Read more
  •  26
    The papers in this special issue are based on presentations delivered at the conference Epistemic Aspects of Many-valued Logics, held at the Institute of Philosophy of the Academy of Sciences of the Czech Republic, in Prague, 2010. All papers consequently revolve around the application of non-classical logical tools—mathematical fuzzy logic and/or probability theory—to epistemological issues.Timothy Williamson employs a modal epistemic logic enriched with probabilities to generalize an argument …Read more
  •  20
    Eliciting Uncertainties: A Two Structure Approach
    Studia Logica 106 (3): 615-636. 2018.
    We recast subjective probabilities by rejecting behaviourist accounts of belief by explicitly distinguishing between judgements of uncertainty and expressions of those judgements. We argue that this entails rejecting that orderings of uncertainty be complete. This in turn leads naturally to several generalizations of the probability calculus. We define probability-like functions over incomplete algebras that reflect a subject’s incomplete judgements of uncertainty. These functions can be further…Read more
  •  17
    Interpretace znalosti v substrukturálních rámcích
    with Michal Peliš
    Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 20 (1): 79-98. 2013.
  •  17
    Fuzzy intensional semantics
    with Libor Běhounek
    Journal of Applied Non-Classical Logics 28 (4): 348-388. 2018.
    The study of weighted structures is one of the important trends in recent computer science. The aim of the article is to provide a weighted, many-valued version of classical intensional semantics formalised in the framework of higher-order fuzzy logics. We illustrate the apparatus on several variants of fuzzy S5-style modalities. The formalism is applicable to a broad array of weighted intensional notions, including alethic, epistemic, or probabilistic modalities, generalised quantifiers, counte…Read more
  •  14
    Logic of change, change of logic
    with Hans Ditmarsch and Brian Hill
    Synthese 171 (2): 227-234. 2009.
  •  14
    A graded semantics for counterfactuals
    with Libor Běhounek
    Synthese 199 (5-6): 11963-11994. 2021.
    This article presents an extension of Lewis’ analysis of counterfactuals to a graded framework. Unlike standard graded approaches, which use the probabilistic framework, we employ that of many-valued logics. Our principal goal is to provide an adequate analysis of the main background notion of Lewis’ approach—the one of the similarity of possible worlds. We discuss the requirements imposed on the analysis of counterfactuals by the imprecise character of similarity and concentrate in particular o…Read more
  •  14
    Epistemic Erotetic Search Scenarios
    with Paweł Łupkowski, Michal Peliš, and Mariusz Urbański
    Logic and Logical Philosophy 27 (3): 301-328. 2018.
    The aim of this paper is to introduce erotetic search scenarios known from Inferential Erotetic Logic by using the framework of epistemic erotetic logic. The key notions used in this system are those of askability and epistemic erotetic implication. Scenarios are supposed to represent all rational strategies of an agent solving the problem posed by the initial question where the interaction with an external information source is seen as a series of updates of the agent’s knowledge.
  •  13
    Analyzing situations where information is partial, incomplete or contradictory has created a demand for quantitative belief measures that are weaker than classic probability theory. In this paper, we compare two frameworks that have been proposed for this task, Dempster-Shafer theory and non-standard probability theory based on Belnap-Dunn logic. We show the two frameworks to assume orthogonal perspectives on informational shortcomings, but also provide a partial correspondence result. Lastly, w…Read more
  •  12
    Reasoning with belief functions over Belnap–Dunn logic
    with Marta Bílková, Sabine Frittella, Daniil Kozhemiachenko, and Sajad Nazari
    Annals of Pure and Applied Logic. forthcoming.
  •  10
    Relevant Agents
    with Marta Bílková, Michal Peliš, and Greg Restall
    In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 22-38. 1998.
  •  9
    On Semantic Games for Łukasiewicz Logic
    with Christian Fermüller
    In Hans van Ditmarsch & Gabriel Sandu (eds.), Jaakko Hintikka on Knowledge and Game Theoretical Semantics, Springer. pp. 263-278. 2018.
    We explore different ways to generalize Hintikka’s classic game theoretic semantics to a many-valued setting, where the unit interval is taken as the set of truth values. In this manner a plethora of characterizations of Łukasiewicz logic arise. Among the described semantic games is Giles’s dialogue and betting game, presented in a manner that makes the relation to Hintikka’s game more transparent. Moreover, we explain a so-called explicit evaluation game and a ‘bargaining game’ variant of it. W…Read more
  •  6
    Towards evaluation games for fuzzy logics
    with Petr Cintula
    In Ondrej Majer, Ahti-Veikko Pietarinen & Tero Tulenheimo (eds.), Games: Unifying Logic, Language, and Philosophy, Springer Verlag. pp. 117--138. 2009.
  •  4
    Relevant Agents
    with Marta Bílková, Michal Peliš, and Greg Restall
    In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 22-38. 1998.
  •  3
    Truth-Maker Semantics for Some Substructural Logics
    In Federico L. G. Faroldi & Frederik Van De Putte (eds.), Kit Fine on Truthmakers, Relevance, and Non-classical Logic, Springer Verlag. pp. 207-222. 2023.
    Fine (J Philos Log 43:549–577, 2014) developed a truthmaker semantics for intuitionistic logic, which is also called exact semantics, since it is based on a relation of exact verification between states and formulas. A natural question arises as to what are the limits of Fine’s approach and whether an exact semantics of similar kind can be constructed for other important non-classical logics. In our paper, we will generalize Fine’s approach and develop an exact semantics for some substructural l…Read more
  •  2
    Two-Layered Logics for Paraconsistent Probabilities
    with Marta Bílková, Sabine Frittella, and Daniil Kozhemiachenko
    In Helle Hvid Hansen, Andre Scedrov & Ruy J. G. B. de Queiroz (eds.), Logic, Language, Information, and Computation: 29th International Workshop, WoLLIC 2023, Halifax, NS, Canada, July 11–14, 2023, Proceedings, Springer Nature Switzerland. pp. 101-117. 2023.
    We discuss two-layered logics formalising reasoning with paraconsistent probabilities that combine the Łukasiewicz [0, 1]-valued logic with Baaz ▵\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\triangle $$\end{document} operator and the Belnap–Dunn logic. The first logic (introduced in [7]) formalises a ‘two-valued’…Read more
  •  2
    Probabilities in possible worlds
    In Hans Rott & Vitezslav Horak (eds.), Possibility and Reality, Walter De Gruyter. pp. 139-148. 2003.
  •  1
    Knowledge Interpretation in Substructural Frames
    with Michal Pelis
    Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 20 79-98. 2013.
  • Teoria zdarzeń sekwencyjnych
    Filozofia Nauki 1. 2002.
    The article deals with the problem of inductive learning and predicting in dynamic processes, which can be formally represented as time series of atomic events. The central notion of sequential event is characterised as a finite subsequence of adjacent atomic events in a series. In the first part of the article an algorythmic model of learning is introduced. The criterion of learning is based on the frequency of a particular sequential event and on the time-distance of its previous occurrences f…Read more
  • Subjektivní pravděpodobnost a realistické možné světy
    Filosoficky Casopis 49 495-505. 2001.
    [Subjective probability and realistic possible worlds]