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  1. Epistemic logic.Vincent Hendricks - 2008 - Stanford Encyclopedia of Philosophy.
    Epistemic logic is the logic of knowledge and belief. It provides insight into the properties of individual knowers, has provided a means to model complicated scenarios involving groups of knowers and has improved our understanding of the dynamics of inquiry.
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  • A study of modal logic with semantics based on rough set theory.Md Aquil Khan, Ranjan & Amal Talukdar - 2024 - Journal of Applied Non-Classical Logics 34 (2):223-247.
    Volume 34, Issue 2-3, June - September 2024.
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  • A Unified Logic for Contingency and Accident.Jie Fan - 2022 - Journal of Philosophical Logic 51 (4):693-720.
    As shown in Fan, there are some similarities/resemblances between contingency and accident. Given this, one may naturally ask if we can unify the two operators to manifest all of their similarities/resemblances. In this article, instead of looking at the interactions between the two operators like in Fan, we turn our attention to the resemblances between the two operators. We extend the unification method in Fan to the current setting. The main results include some model-theoretical ones, such as expressivity, frame definability, (...)
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  • Logics for propositional determinacy and independence.Valentin Goranko & Antti Kuusisto - 2018 - Review of Symbolic Logic 11 (3):470-506.
    This paper investigates formal logics for reasoning about determinacy and independence. Propositional Dependence Logic D and Propositional Independence Logic I are recently developed logical systems, based on team semantics, that provide a framework for such reasoning tasks. We introduce two new logics L_D and L_I, based on Kripke semantics, and propose them as alternatives for D and I, respectively. We analyse the relative expressive powers of these four logics and discuss the way these systems relate to natural language. We argue (...)
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  • A logic of goal-directed knowing how.Yanjing Wang - 2018 - Synthese 195 (10):4419-4439.
    In this paper, we propose a decidable single-agent modal logic for reasoning about goal-directed “knowing how”, based on ideas from linguistics, philosophy, modal logic, and automated planning in AI. We first define a modal language to express “I know how to guarantee \ given \” with a semantics based not on standard epistemic models but on labeled transition systems that represent the agent’s knowledge of his own abilities. The semantics is inspired by conformant planning in AI. A sound and complete (...)
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  • Non-contingency in a Paraconsistent Setting.Daniil Kozhemiachenko & Liubov Vashentseva - forthcoming - Logic Journal of the IGPL.
    We study an extension of first-degree entailment (FDE) by Dunn and Belnap with a non-contingency operator |$\blacktriangle \phi $| which is construed as ‘|$\phi $| has the same value in all accessible states’ or ‘all sources give the same information on the truth value of |$\phi $|’. We equip this logic dubbed |$\textbf {K}^\blacktriangle _{\textbf {FDE}}$| with frame semantics and show how the bi-valued models can be interpreted as interconnected networks of Belnapian databases with the |$\blacktriangle $| operator modelling search (...)
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  • A lightweight epistemic logic and its application to planning.Martin C. Cooper, Andreas Herzig, Faustine Maffre, Frédéric Maris, Elise Perrotin & Pierre Régnier - 2021 - Artificial Intelligence 298 (C):103437.
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  • Logics of (In)sane and (Un)reliable Beliefs.Jie Fan - 2022 - Logic Journal of the IGPL 30 (1):78-100.
    Inspired by an interesting quotation from the literature, we propose four modalities, called ‘sane belief’, ‘insane belief’, ‘reliable belief’ and ‘unreliable belief’, and introduce logics with each operator as the modal primitive. We show that the four modalities constitute a square of opposition, which indicates some interesting relationships among them. We compare the relative expressivity of these logics and other related logics, including a logic of false beliefs from the literature. The four main logics are all less expressive than the (...)
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  • Tableaux for essence and contingency.Giorgio Venturi & Pedro Teixeira Yago - 2021 - Logic Journal of the IGPL 29 (5):719-738.
    We offer tableaux systems for logics of essence and accident and logics of non-contingency, showing their soundness and completeness for Kripke semantics. We also show an interesting parallel between these logics based on the semantic insensitivity of the two non-normal operators by which these logics are expressed.
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  • A New Framework for Epistemic Logic.Yanjing Wang - 2017 - In Proceedings of TARK 2017. EPTCS. pp. 515-534.
    Recent years witnessed a growing interest in non-standard epistemic logics of knowing whether, knowing how, knowing what, knowing why and so on. The new epistemic modalities introduced in those logics all share, in their semantics, the general schema of ∃x◻φ, e.g., knowing how to achieve φ roughly means that there exists a way such that you know that it is a way to ensure that φ. Moreover, the resulting logics are decidable. Inspired by those particular logics, in this work, we (...)
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  • "Knowing value" logic as a normal modal logic.Tao Gu & Yanjing Wang - 2016 - In Lev Beklemishev, Stéphane Demri & András Máté (eds.), Advances in Modal Logic, Volume 11. CSLI Publications. pp. 362-381.
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  • Logics of True Belief.Yuanzhe Yang - 2024 - Notre Dame Journal of Formal Logic 65 (1):55-80.
    In epistemic logic, the beliefs of an agent are modeled in a way very similar to knowledge, except that they are fallible. Thus, the pattern of an agent’s true beliefs is an interesting subject to study. In this paper, we conduct a systematic study on a novel modal logic with the bundled operator ⊡ϕ:=□ϕ∧ϕ as the only primitive modality, where ⊡ captures the notion of true belief. With the help of a novel notion of ⊡-bisimulation, we characterize the expressivity of (...)
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  • A Logic of Temporal Contingency.Jie Fan - 2024 - Erkenntnis 89 (7):2611-2640.
    We propose a logic of temporal contingency, which has operators of past and future contingency as primitive modalities. This logic is less expressive than standard temporal logic over the class of bidirectional frames, and cannot define some basic frame properties such as bidirectionality and transitivity. We present a minimal system based on two key ‘bridge axioms’ and a bimodal version of a so-called ‘almost definability’ schema in the literature. The completeness proof is highly nontrivial due to the requirement that the (...)
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  • Bisimulations for Knowing How Logics.Raul Fervari, Fernando R. Velázquez-Quesada & Yanjing Wang - 2022 - Review of Symbolic Logic 15 (2):450-486.
    As a new type of epistemic logics, the logics of knowing how capture the high-level epistemic reasoning about the knowledge of various plans to achieve certain goals. Existing work on these logics focuses on axiomatizations; this paper makes the first study of their model theoretical properties. It does so by introducing suitable notions of bisimulation for a family of five knowing how logics based on different notions of plans. As an application, we study and compare the expressive power of these (...)
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  • A Family of Neighborhood Contingency Logics.Jie Fan - 2019 - Notre Dame Journal of Formal Logic 60 (4):683-699.
    This article proposes the axiomatizations of contingency logics of various natural classes of neighborhood frames. In particular, by defining a suitable canonical neighborhood function, we give sound and complete axiomatizations of monotone contingency logic and regular contingency logic, thereby answering two open questions raised by Bakhtiari, van Ditmarsch, and Hansen. The canonical function is inspired by a function proposed by Kuhn in 1995. We show that Kuhn’s function is actually equal to a related function originally given by Humberstone.
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  • Planning-based knowing how: A unified approach.Yanjun Li & Yanjing Wang - 2021 - Artificial Intelligence 296 (C):103487.
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  • A Modal Logic of Supervenience.Jie Fan - 2019 - Notre Dame Journal of Formal Logic 60 (2):283-309.
    Inspired by the supervenience-determined consequence relation and the semantics of agreement operator, we introduce a modal logic of supervenience, which has a dyadic operator of supervenience as a sole modality. The semantics of supervenience modality very naturally correspond to the supervenience-determined consequence relation, in a quite similar way that the strict implication corresponds to the inference-determined consequence relation. We show that this new logic is more expressive than the modal logic of agreement, by proposing a notion of bisimulation for the (...)
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  • Knowledge and ignorance in Belnap–Dunn logic.Daniil Kozhemiachenko & Liubov Vashentseva - forthcoming - Logic Journal of the IGPL.
    In this paper, we argue that the usual approach to modelling knowledge and belief with the necessity modality |$\Box $| does not produce intuitive outcomes in the framework of the Belnap–Dunn logic (⁠|$\textsf{BD}$|⁠, alias |$\textbf{FDE}$|—first-degree entailment). We then motivate and introduce a nonstandard modality |$\blacksquare $| that formalizes knowledge and belief in |$\textsf{BD}$| and use |$\blacksquare $| to define |$\bullet $| and |$\blacktriangledown $| that formalize the unknown truth and ignorance as not knowing whether, respectively. Moreover, we introduce another modality (...)
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  • An Egocentric Logic of Knowing How to Tell Them Apart.Pavel Naumov & T. A. O. Jia - forthcoming - Journal of Symbolic Logic:1-33.
    Traditionally, the formulae in modal logic express properties of possible worlds. Prior introduced “egocentric” logics that capture properties of agents rather than of possible worlds. In such a setting, the article proposes the modality “know how to tell apart” and gives a complete logical system describing the interplay between this modality and the knowledge modality. An important contribution of this work is a new matrix-based technique for proving completeness theorems in an egocentric setting.
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  • Some Notes on Dyadic Contingency.Jie Fan - 2023 - Journal of Logic, Language and Information 32 (2):209-217.
    In a recent work, Pizzi proposes a notion of dyadic non-contingency, and then gives an axiomatic system of dyadic non-contingency named \(\text {KD}\Delta ^2\), which is shown to be translationally equivalent to the deontic system KD and has the minimal system \(\text {K}\Delta \) of monadic contingency as a fragment. However, the reason why he defines dyadic non-contingency like that is unclear. In this article, inspired by the notion of relativized knowing-value in the literature, we give a plausible explanation for (...)
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  • Model Theoretical Aspects of Weakly Aggregative Modal Logic.Jixin Liu, Yifeng Ding & Yanjing Wang - 2022 - Journal of Logic, Language and Information 31 (2):261-286.
    Weakly Aggregative Modal Logic ) is a collection of disguised polyadic modal logics with n-ary modalities whose arguments are all the same. \ has interesting applications on epistemic logic, deontic logic, and the logic of belief. In this paper, we study some basic model theoretical aspects of \. Specifically, we first give a van Benthem–Rosen characterization theorem of \ based on an intuitive notion of bisimulation. Then, in contrast to many well known normal or non-normal modal logics, we show that (...)
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  • Strong Noncontingency: On the Modal Logics of an Operator Expressively Weaker Than Necessity.Jie Fan - 2019 - Notre Dame Journal of Formal Logic 60 (3):407-435.
    Operators can be compared in at least two respects: expressive strength and deductive strength. Inspired by Hintikka’s treatment of question embedding verbs, the variations of noncontingency operator, and also the various combinations of modal operators and Boolean connectives, we propose a logic with strong noncontingency operator as the only primitive modality. The novel operator is deductively but not expressively stronger than both noncontingency operator and essence operator, and expressively but not deductively weaker than the necessity operator. The frame-definability power of (...)
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  • Axiomatizing Rumsfeld Ignorance.Jie Fan - 2023 - Journal of Philosophical Logic 53 (1):79-97.
    In a recent paper, Kit Fine presents some striking results concerning the logical properties of (first-order) ignorance, second-order ignorance and Rumsfeld ignorance. However, Rumsfeld ignorance is definable in terms of ignorance, which makes some existing results and the axiomatization problem trivial. A main reason is that the accessibility relations for the implicit knowledge operator contained in the packaged operators of ignorance and Rumsfeld ignorance are the same. In this work, we assume the two accessibility relations to be different so that (...)
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  • Propositional quantification in logics of contingency.Hans van Ditmarsch & Jie Fan - 2016 - Journal of Applied Non-Classical Logics 26 (1):81-102.
    In this work we define contingency logic with arbitrary announcement. In contingency logic, the primitive modality contingency formalises that a proposition may be true but also may be false, so that if it is non-contingent then it is necessarily true or necessarily false. To this logic one can add dynamic operators to describe change of contingency. Our logic has operators for public announcement and operators for arbitrary public announcement, as in the dynamic epistemic logic called arbitrary public announcement logic. However, (...)
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  • A Family of Kripke Contingency Logics.Jie Fan - 2020 - Theoria 86 (4):482-499.
    In Fan's 2019 article, “Symmetric Contingency Logic with Unlimitedly Many Modalities”, it is left as an open question in Fan (2019b) how to (completely) axiomatize contingency logic over the class of symmetric and transitive frames, and conjectured that is the desired axiomatization. In the current article, we show that the conjecture is false, and then propose a desired axiomatization, thereby answering the open question. Beyond these results, we also present a family of axiomatizations of contingency logic over Kripke frames.
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  • Free Choice in Modal Inquisitive Logic.Karl Nygren - 2023 - Journal of Philosophical Logic 52 (2):347-391.
    This paper investigates inquisitive extensions of normal modal logic with an existential modal operator taken as primitive. The semantics of the existential modality is generalized to apply to questions, as well as statements. When the generalized existential modality is applied to a question, the result is a statement that roughly expresses that each way of resolving the question is consistent with the available information. I study the resulting logic both from a semantic and from a proof-theoretic point of view. I (...)
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  • Bimodal Logic with Contingency and Accident: Bisimulation and Axiomatizations.Jie Fan - 2021 - Logica Universalis 15 (2):123-147.
    In this paper, a suitable notion of bisimulation is proposed for the bimodal logic with contingency and accident. We obtain several van Benthem Characterization Theorems, and axiomatize the bimodal logic over the class of Eulidean frames and over some more restricted classes, showing their strong completeness via a novel strategy, thereby answering two open questions raised in the literature. With the new bisimulation notion, we also correct an error in the expressivity results in the literature.
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  • Bimodal Logics with Contingency and Accident.Jie Fan - 2019 - Journal of Philosophical Logic 48 (2):425-445.
    Contingency and accident are two important notions in philosophy and philosophical logic. Their meanings are so close that they are mixed up sometimes, in both daily life and academic research. This indicates that it is necessary to study them in a unified framework. However, there has been no logical research on them together. In this paper, we propose a language of a bimodal logic with these two concepts, investigate its model-theoretical properties such as expressivity and frame definability. We axiomatize this (...)
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