•  11
    Epistemic Logics for Relevant Reasoners
    Journal of Philosophical Logic 53 (5): 1383-1411. 2024.
    We present a neighbourhood-style semantic framework for modal epistemic logic modelling agents who process information using relevant logic. The distinguishing feature of the framework in comparison to relevant modal logic is that the environment the agent is situated in is assumed to be a classical possible world. This framework generates two-layered logics combining classical logic on the propositional level with relevant logic in the scope of modal operators. Our main technical result is a ge…Read more
  • Logica Yearbook 2022 (edited book)
    College Publications. 2023.
  •  21
    New Directions in Relevant Logic (edited book)
    with Andrew Tedder and Shawn Standefer
    Springer. 2024.
    This book brings together contemporary work on relevant logics to showcase the recent progress of the field and set the stage for future research. The papers in the volume contribute to the formal and philosophical development of the field. They include contributions from different traditions and approaches ranging from philosophical discussions of the foundations of relevant, and related kinds of non-classical, logic to mathematical work concerning open technical problems in the field. This is …Read more
  •  18
    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
  •  36
    Hyperintensional models for non-congruential modal logics
    Logic Journal of the IGPL. forthcoming.
    In this work, we illustrate applications of a semantic framework for non-congruential modal logic based on hyperintensional models. We start by discussing some philosophical ideas behind the approach; in particular, the difference between the set of possible worlds in which a formula is true (its intension) and the semantic content of a formula (its hyperintension), which is captured in a rigorous way in hyperintensional models. Next, we rigorously specify the approach and provide a fundamental …Read more
  •  13
    Combining relevant and classical modal logic is an approach to overcoming the logical omniscience problem and related issues that goes back at least to Levesque’s well known work in the 1980s. The present authors have recently introduced a variant of Levesque’s framework where explicit beliefs concerning conditional propositions can be formalized. However, our framework did not offer a formalization of implicit belief in addition to explicit belief. In this paper we provide such a formalization.…Read more
  •  23
    The Logica Yearbook 2021 (edited book)
    College Publications. 2022.
    This volume of the Logica Yearbook series brings together articles based on selected abstracts accepted for presentation at the annual international symposium Logica 2021, in Hejnice, the Czech Republic. The articles range over mathematical and philosophical logic, history and philosophy of logic, and the analysis of natural language.
  •  42
    In this paper we discuss whether the relation between formulas in the relating model can be directly introduced into the language of relating logic, and present some stances on that problem. Other questions in the vicinity, such as what kind of functor would be the incorporated relation, or whether the direct incorporation of the relation into the language of relating logic is really needed, will also be addressed.
  •  11
    One way to model epistemic states of agents more realistically is to represent these states by sets of situations rather than possible worlds. In this paper we discuss representations of epistemic update in terms of situations. After linking epistemic update based on deleting epistemic accessibility arrows with update of situations, we discuss two specific kinds of public epistemic update; monotonic update in intuitionistic dynamic epistemic logic, and non-monotonic update in substructural dynam…Read more
  •  37
    The Logica Yearbook 2020 (edited book)
    with Martin Blicha
    College Publications. 2021.
    This volume of the Logica Yearbook series brings together articles based on selected abstracts accepted for presentation at the annual international symposium Logica 2020, Hejnice, the Czech Republic, which was cancelled due to the Covid-19 pandemic. The articles range over mathematical and philosophical logic, history and philosophy of logic, and the analysis of natural language.
  •  37
    Inquisitive Propositional Dynamic Logic
    Journal of Logic, Language and Information 30 (1): 91-116. 2021.
    This paper combines propositional dynamic logic ) with propositional inquisitive logic ). The result of this combination is a logical system \ that conservatively extends both \ and \, and, moreover, allows for an interaction of the question-forming operator from \ with the structured modalities from \. We study this system from a semantic as well as a syntactic point of view. These two perspectives are linked via a completeness proof, which also shows that \ is decidable.
  •  36
    Correction to: Lambek Calculus with Conjugates
    Studia Logica 109 (3): 471-471. 2020.
    We, the authors, would like to thank Guillaume Aucher for informing us of his “Displaying Updates in Logic”, published in the Journal of Logic and Computation, 26:1865-1912.
  •  32
    Lambek Calculus with Conjugates
    Studia Logica 109 (3): 447-470. 2020.
    We study an expansion of the Distributive Non-associative Lambek Calculus with conjugates of the Lambek product operator and residuals of those conjugates. The resulting logic is well-motivated, under-investigated and difficult to tackle. We prove completeness for some of its fragments and establish that it is decidable. Completeness of the logic is an open problem; some difficulties with applying the usual proof method are discussed.
  •  24
    The Logica Yearbook 2019 (edited book)
    with Martin Blicha
    College Publications. 2020.
    This volume of the Logica Yearbook series brings together articles presented at the annual international symposium Logica 2019, Hejnice, the Czech Republic. The articles range over mathematical and philosophical logic, history and philosophy of logic, and the analysis of natural language.
  •  18
    The Logica Yearbook 2018 (edited book)
    with Martin Blicha
    College Publications. 2019.
    This volume of the Logica Yearbook series brings together articles presented at the annual international symposium Logica 2018, Hejnice, the Czech Republic. The articles range over mathematical and philosophical logic, history and philosophy of logic, and the analysis of natural language.
  •  39
    From positive PDL to its non-classical extensions
    Logic Journal of the IGPL 27 (4): 522-542. 2019.
    We provide a complete binary implicational axiomatization of the positive fragment of propositional dynamic logic. The intended application of this result are completeness proofs for non-classical extensions of positive PDL. Two examples are discussed in this article, namely, a paraconsistent extension with modal De Morgan negation and a substructural extension with the residuated operators of the non-associative Lambek calculus. Informal interpretations of these two extensions are outlined.
  •  93
    Hyperintensional logics for everyone
    Synthese 198 (2): 933-956. 2019.
    We introduce a general representation of unary hyperintensional modalities and study various hyperintensional modal logics based on the representation. It is shown that the major approaches to hyperintensionality known from the literature, that is state-based, syntactic and structuralist approaches, all correspond to special cases of the general framework. Completeness results pertaining to our hyperintensional modal logics are established.
  •  16
    Propositional dynamic logic with belnapian truth values
    In Lev Beklemishev, Stéphane Demri & András Máté (eds.), Advances in Modal Logic, Volume 11, Csli Publications. pp. 503-519. 2016.
  •  33
    On What You Cannot Be Mistaken About?
    Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 18 (3): 351-362. 2011.
    The paper sketches an analysis of the notion of a self-fulfilling belief in terms of doxastic modal logic. We point out a connection between self-fulfilling beliefs and Moore’s paradox. Then we look at self-fulfilling beliefs in the context of neighborhood semantics. We argue that the analysis of several interesting self-fulfilling beliefs has to make essential use of propositional quantification.
  •  37
    An Outline of a Substructural Model of BTA Belief
    Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 20 (2): 160-170. 2013.
    The paper outlines an epistemic logic based on the proof theory of substructural logics. The logic is a formal model of belief that i) is based on true assumptions (BTA belief) and ii) does not suffer from the usual omniscience properties.
  • Implication and Three Types of Meaning Connection
    Filozofia 64 (4): 339-345. 2009.
    The primary aim of the paper is to introduce a new notion of relevance of the antecedent of a true implication statement to its consequent, and to sketch a formalization of the new notion. The formalization is set up in the framework of the so called Logic of Strict Processes , as articulated by the author in collaboration with J. Podroužek. Their approach to the relevance is presented as a natural part of a wider specter of logics, including modal and relevance logics. The formalization is comp…Read more
  •  29
    The paper introduces a new kind of models for the logic of proofs LP, the group justification models. While being an elaboration of Fitting models, the group justification models are a special case of the models of general awareness. Soundness and completeness results of LP with respect to the new semantics are established. The paper also offers an interpretation of the group models, which pertains to awareness and group epistemic dynamics.
  •  65
    Substructural epistemic logics
    Journal of Applied Non-Classical Logics 25 (3): 256-285. 2015.
    The article introduces substructural epistemic logics of belief supported by evidence. The logics combine normal modal epistemic logics with distributive substructural logics. Pieces of evidence are represented by points in substructural models and availability of evidence is modelled by a function on the point set. The main technical result is a general completeness theorem. Axiomatisations are provided by means of two-sorted Hilbert-style calculi. It is also shown that the framework presents a…Read more
  •  98
    C. I. Lewis on Possible Worlds
    History and Philosophy of Logic 30 (3): 283-291. 2009.
    This article opposes a view widely accepted in studies concerning the history of modal logic, according to which (i) the approach of C. I. Lewis towards constructing modern modal logic was purely syntactical (i.e. limited to the construction of axiomatic systems S1-S5 of propositional modal logic), and (ii) the notion of a possible world was incorporated into modern logic and philosophy mainly by authors such as Rudolf Carnap and Saul Kripke. The article presents Lewis' definition of a possible …Read more
  •  15
    Action frames for weak relevant logics
    In Pavel Arazim & Michal Dancak (eds.), The Logica Yearbook 2014, College Publications. pp. 267-279. 2015.
    The article introduces extended models for the propositional dynamic logic PDL. In extended models, valuation assigns to every state a set of atomic formulas and a PDL program. The program is informally construed as an action preferred by a contextually fixed agent. PDL is then extended by introducing a conditional connective expressing partial correctness claims. The main contribution of the article is the observation that the partial correctness conditional is in fact a substructural implicati…Read more
  • Kant and Frege on analyticity
    Filozofia 62 (4): 336-347. 2007.
    The question, whether there is a sharp difference between an analytic and a synthetic proposition, is one of the famous philosophical topics of the 20th century. The question, however, urges one to ask following questions: "What is an analytic proposition?", or „What is a synthetic proposition?“. The aim of the paper is to contribute to the discussions of the analyticity in that it tries to answer the first of the two. However, the author does not offer his own conception of analyticity. He rath…Read more
  •  25
    Relating logics of justification and evidence
    In Punčochář Vít & Dančák Michal (eds.), The Logica Yearbook 2013, College Publications. pp. 207-222. 2014.
    The paper relates evidence and justification logics, both philosophically and technically. On the philosophical side, it is suggested that the difference between the approaches to evidence in the two families of logics can be explained as a result of their focusing on two different notions of support provided by evidence. On the technical side, a justification logic with operators pertaining to both kinds of support is shown to be sound and complete with respect to a special class of awareness m…Read more
  • The paper offers an argument against Kripke’s assertion, that it is valid for all names of natural species, that they have no connotations. The argumentation has is roots in the semantic conception of S. Kripke as articulated in his Naming and necessity. i.e., it is an „argument from inside“ the conception itself. The argument consists of two parts: setting the conditions under which the name of a natural species has a connotation; constructing a situation, in which these conditions are fulfille…Read more
  •  17
    Information, awareness and substructural logics
    In Leonid Libkin, Ulrich Kohlenbach & Ruy de Queiroz (eds.), Logic, Language, Information and Computation (Lecture Notes in Computer Science 8071), Springer. pp. 266-281. 2013.
    The paper outlines a generalisation of the awareness-based epistemic semantics by Fagin and Halpern. Awareness is construed as a relation between agents and pieces of information instead of formulas. The main motive for introducing the generalisation is that it shows substructural logics to be a natural component of information-based epistemic logic: substructural logics can be seen as describing the logical behaviour of pieces of information. Substructural epistemic logics are introduced and so…Read more