•  115
    Contingency and Knowing Whether
    Review of Symbolic Logic 8 (1): 75-107. 2015.
    A proposition is noncontingent, if it is necessarily true or it is necessarily false. In an epistemic context, ‘a proposition is noncontingent’ means that you know whether the proposition is true. In this paper, we study contingency logic with the noncontingency operator? but without the necessity operator 2. This logic is not a normal modal logic, because?→ is not valid. Contingency logic cannot define many usual frame properties, and its expressive power is weaker than that of basic modal logi…Read more
  •  73
    Bimodal Logics with Contingency and Accident
    Journal of Philosophical Logic 48 (2): 425-445. 2019.
    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.…Read more
  •  60
    A Modal Logic of Supervenience
    Notre Dame Journal of Formal Logic 60 (2): 283-309. 2019.
    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 th…Read more
  •  54
    Strong Noncontingency: On the Modal Logics of an Operator Expressively Weaker Than Necessity
    Notre Dame Journal of Formal Logic 60 (3): 407-435. 2019.
    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 expressive…Read more
  •  42
    Propositional quantification in logics of contingency
    Journal of Applied Non-Classical Logics 26 (1): 81-102. 2016.
    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…Read more
  •  37
    Axiomatizing Rumsfeld Ignorance
    Journal of Philosophical Logic 53 (1): 79-97. 2023.
    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 assum…Read more
  •  34
    A Unified Logic for Contingency and Accident
    Journal of Philosophical Logic 51 (4): 693-720. 2022.
    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 a…Read more
  •  33
    A Logic for Disjunctive Ignorance
    Journal of Philosophical Logic 50 (6): 1293-1312. 2021.
    In this paper, we introduce a notion of ‘disjunctive ignorance’, which is a weak combination of two forms of ignorance in the literature. We propose a logical language with ‘disjunctive ignorance’ as a sole modality, explore the logical properties of this notion and its related notions, and axiomatize it over various frame classes. By finding suitable reduction axioms, we extend the results to the case of public announcements and apply it to Moore-like sentences.
  •  31
    In this article, we study logics of unknown truths and false beliefs under neighborhood semantics. We compare the relative expressivity of the two logics. It turns out that they are incomparable over various classes of neighborhood models, and the combination of the two logics are equally expressive as standard modal logic over any class of neighborhood models. We propose morphisms for each logic, which can help us explore the frame definability problem, show a general soundness and completeness…Read more
  •  28
    Symmetric Contingency Logic with Unlimitedly Many Modalities
    Journal of Philosophical Logic 48 (5): 851-866. 2019.
    The completeness of the axiomatization of contingency logic over symmetric frames has been thought of as a nontrivial job, the unimodal case of which cannot be generalized to the finitely multimodal case, which in turn cannot be generalized to the infinitely multimodal case. This paper deals with the completeness of symmetric contingency logic with unlimitedly many modalities, no matter whether the set of modalities is finite or infinite.
  •  26
    A Family of Neighborhood Contingency Logics
    Notre Dame Journal of Formal Logic 60 (4): 683-699. 2019.
    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 …Read more
  •  25
    Some Notes on Dyadic Contingency
    Journal of Logic, Language and Information 32 (2): 209-217. 2023.
    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 pl…Read more
  •  24
    A Family of Kripke Contingency Logics
    Theoria 86 (4): 482-499. 2020.
    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 cont…Read more
  •  22
    Logics of (In)sane and (Un)reliable Beliefs
    Logic Journal of the IGPL 30 (1): 78-100. 2022.
    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 fo…Read more
  •  18
    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…Read more
  •  16
    A Logic of Temporal Contingency
    Erkenntnis 1-30. forthcoming.
    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 du…Read more
  •  6
    Notions of unknown truths and unknowable truths are important in formal epistemology, which are related to each other in e.g. Fitch’s paradox of knowability. Although there have been some logical research on the notion of unknown truths and some philosophical discussion on the two notions, there seems to be no logical research on unknowable truths. In this paper, we propose a logic of unknowable truths, investigate the logical properties of unknown truths and unknowable truths, which includes th…Read more