20 found
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  1.  28
    A Deterministic Weakening of Belnap–Dunn Logic.Minghui Ma & Yuanlei Lin - 2019 - Studia Logica 107 (2):283-312.
    A deterministic weakening \ of the Belnap–Dunn four-valued logic \ is introduced to formalize the acceptance and rejection of a proposition at a state in a linearly ordered informational frame with persistent valuations. The logic \ is formalized as a sequent calculus. The completeness and decidability of \ with respect to relational semantics are shown in terms of normal forms. From an algebraic perspective, the class of all algebras for \ is described, and found to be a subvariety of Berman’s (...)
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  2.  31
    Gamma Graph Calculi for Modal Logics.Minghui Ma & Ahti-Veikko Pietarinen - 2018 - Synthese 195 (8):3621-3650.
    We describe Peirce’s 1903 system of modal gamma graphs, its transformation rules of inference, and the interpretation of the broken-cut modal operator. We show that Peirce proposed the normality rule in his gamma system. We then show how various normal modal logics arise from Peirce’s assumptions concerning the broken-cut notation. By developing an algebraic semantics we establish the completeness of fifteen modal logics of gamma graphs. We show that, besides logical necessity and possibility, Peirce proposed an epistemic interpretation of the (...)
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  3.  29
    Let Us Investigate! Dynamic Conjecture-Making as the Formal Logic of Abduction.Minghui Ma & Ahti-Veikko Pietarinen - 2018 - Journal of Philosophical Logic 47 (6):913-945.
    We present a dynamic approach to Peirce’s original construal of abductive logic as a logic of conjecture making, and provide a new decidable, contraction-free and cut-free proof system for the dynamic logic of abductive inferences with neighborhood semantics. Our formulation of the dynamic logic of abduction follows the philosophical and scientific track that led Peirce to his late, post-1903 characterization of abductive conclusions as investigands, namely invitations to investigate propositions conjectured at the level of pre-beliefs.
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  4.  33
    Peirce’s Calculi for Classical Propositional Logic.Minghui Ma & Ahti-Veikko Pietarinen - 2020 - Review of Symbolic Logic 13 (3):509-540.
    This article investigates Charles Peirce’s development of logical calculi for classical propositional logic in 1880–1896. Peirce’s 1880 work on the algebra of logic resulted in a successful calculus for Boolean algebra. This calculus, denoted byPC, is here presented as a sequent calculus and not as a natural deduction system. It is shown that Peirce’s aim was to presentPCas a sequent calculus. The law of distributivity, which Peirce states in 1880, is proved using Peirce’s Rule, which is a residuation, inPC. The (...)
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  5.  28
    Countably Many Weakenings of Belnap–Dunn Logic.Minghui Ma & Yuanlei Lin - 2020 - Studia Logica 108 (2):163-198.
    Every Berman’s variety \ which is the subvariety of Ockham algebras defined by the equation \ and \) determines a finitary substitution invariant consequence relation \. A sequent system \ is introduced as an axiomatization of the consequence relation \. The system \ is characterized by a single finite frame \ under the frame semantics given for the formal language. By the duality between frames and algebras, \ can be viewed as a \-valued logic as it is characterized by a (...)
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  6.  15
    Polarity Semantics for Negation as a Modal Operator.Yuanlei Lin & Minghui Ma - 2020 - Studia Logica 108 (5):877-902.
    The minimal weakening \ of Belnap-Dunn logic under the polarity semantics for negation as a modal operator is formulated as a sequent system which is characterized by the class of all birelational frames. Some extensions of \ with additional sequents as axioms are introduced. In particular, all three modal negation logics characterized by a frame with a single state are formalized as extensions of \. These logics have the finite model property and they are decidable.
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  7.  17
    Algebraic Semantics and Model Completeness for Intuitionistic Public Announcement Logic.Minghui Ma, Alessandra Palmigiano & Mehrnoosh Sadrzadeh - 2014 - Annals of Pure and Applied Logic 165 (4):963-995.
    In the present paper, we start studying epistemic updates using the standard toolkit of duality theory. We focus on public announcements, which are the simplest epistemic actions, and hence on Public Announcement Logic without the common knowledge operator. As is well known, the epistemic action of publicly announcing a given proposition is semantically represented as a transformation of the model encoding the current epistemic setup of the given agents; the given current model being replaced with its submodel relativized to the (...)
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  8.  18
    Proof Analysis of Peirce’s Alpha System of Graphs.Minghui Ma & Ahti-Veikko Pietarinen - 2017 - Studia Logica 105 (3):625-647.
    Charles Peirce’s alpha system \ is reformulated into a deep inference system where the rules are given in terms of deep graphical structures and each rule has its symmetrical rule in the system. The proof analysis of \ is given in terms of two embedding theorems: the system \ and Brünnler’s deep inference system for classical propositional logic can be embedded into each other; and the system \ and Gentzen sequent calculus \ can be embedded into each other.
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  9.  15
    Labelled Tableau Systems for Some Subintuitionistic Logics.Minghui Ma - 2019 - Logica Universalis 13 (2):273-288.
    Labelled tableau systems are developed for subintuitionistic logics \, \ and \. These subintuitionistic logics are embedded into corresponding normal modal logics. Hintikka’s model systems are applied to prove the completeness of labelled tableau systems. The finite model property, decidability and disjunction property are obtained by labelled tableau method.
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  10.  28
    Sequent Calculi for Semi-De Morgan and De Morgan Algebras.Minghui Ma & Fei Liang - 2018 - Studia Logica 106 (3):565-593.
    A contraction-free and cut-free sequent calculus \ for semi-De Morgan algebras, and a structural-rule-free and single-succedent sequent calculus \ for De Morgan algebras are developed. The cut rule is admissible in both sequent calculi. Both calculi enjoy the decidability and Craig interpolation. The sequent calculi are applied to prove some embedding theorems: \ is embedded into \ via Gödel–Gentzen translation. \ is embedded into a sequent calculus for classical propositional logic. \ is embedded into the sequent calculus \ for intuitionistic (...)
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  11.  10
    Goldblatt-Thomason-Style Theorems for Graded Modal Language.Katsuhiko Sano & Minghui Ma - 2010 - In Lev Beklemishev, Valentin Goranko & Valentin Shehtman (eds.), Advances in Modal Logic, Volume 8. CSLI Publications. pp. 330-349.
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  12.  6
    Belnap–Dunn Modal Logic with Value Operators.Yuanlei Lin & Minghui Ma - 2020 - Studia Logica 109 (4):759-789.
    The language of Belnap–Dunn modal logic \ expands the language of Belnap–Dunn four-valued logic with the modal operator \. We introduce the polarity semantics for \ and its two expansions \ and \ with value operators. The local finitary consequence relation \ in the language \ with respect to the class of all frames is axiomatized by a sequent system \ where \. We prove by using translations between sequents and formulas that these languages under the polarity semantics have the (...)
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  13.  45
    Gentzen Sequent Calculi for Some Intuitionistic Modal Logics.Zhe Lin & Minghui Ma - 2019 - Logic Journal of the IGPL 27 (4):596-623.
    Intuitionistic modal logics are extensions of intuitionistic propositional logic with modal axioms. We treat with two modal languages ${\mathscr{L}}_\Diamond $ and $\mathscr{L}_{\Diamond,\Box }$ which extend the intuitionistic propositional language with $\Diamond $ and $\Diamond,\Box $, respectively. Gentzen sequent calculi are established for several intuitionistic modal logics. In particular, we introduce a Gentzen sequent calculus for the well-known intuitionistic modal logic $\textsf{MIPC}$. These sequent calculi admit cut elimination and subformula property. They are decidable.
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  14.  8
    A Paraconsistent Conditional Logic.Minghui Ma & Chun-Ting Wong - 2020 - Journal of Philosophical Logic 49 (5):883-903.
    We develop a paraconsistent logic by introducing new models for conditionals with acceptive and rejective selection functions which are variants of Chellas’ conditional models. The acceptance and rejection conditions are substituted for truth conditions of conditionals. The paraconsistent conditional logic is axiomatized by a sequent system \ which is an extension of the Belnap-Dunn four-valued logic with a conditional operator. Some acceptive extensions of \ are shown to be sound and complete. We also show the finite acceptive model property and (...)
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  15.  21
    A Three-Valued Fregean Quantification Logic.Minghui Ma & Yuanlei Lin - 2019 - Journal of Philosophical Logic 48 (2):409-423.
    Kripke’s Fregean quantification logic FQ fails to formalize the usual first-order logic with identity due to the interpretation of the conditional operator. Motivated by Kripke’s syntax and semantics, the three-valued Fregean quantification logic FQ3 is proposed. This three valued logic differs from Kleene and Łukasiewicz’s three-valued logics. The logic FQ3 is decidable. A sound and complete Hilbert-style axiomatic system for the logic FQ3 is presented.
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  16.  22
    Dynamic Graded Epistemic Logic.Minghui Ma & Hans van Ditmarsch - 2019 - Review of Symbolic Logic 12 (4):663-684.
    Graded epistemic logic is a logic for reasoning about uncertainties. Graded epistemic logic is interpreted on graded models. These models are generalizations of Kripke models. We obtain completeness of some graded epistemic logics. We further develop dynamic extensions of graded epistemic logics, along the framework of dynamic epistemic logic. We give an extension with public announcements, i.e., public events, and an extension with graded event models, a generalization also including nonpublic events. We present complete axiomatizations for both logics.
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  17.  3
    Lattices of Finitely Alternative Normal Tense Logics.Minghui Ma & Qian Chen - forthcoming - Studia Logica:1-26.
    A finitely alternative normal tense logic \ is a normal tense logic characterized by frames in which every point has at most n future alternatives and m past alternatives. The structure of the lattice \\) is described. There are \ logics in \\) without the finite model property, and only one pretabular logic in \\). There are \ logics in \\) which are not finitely axiomatizable. For \, there are \ logics in \\) without the FMP, and infinitely many pretabular (...)
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  18.  15
    Peirce's Logical Graphs for Boolean Algebras and Distributive Lattices.Minghui Ma - 2018 - Transactions of the Charles S. Peirce Society 54 (3):320.
    Peirce introduced Existential Graphs in late 1896, and they were systematically investigated in his 1903 Lowell Lectures. Alpha graphs for classical propositional logic constitute the first part of EGs. The second and the third parts are the beta graphs for first-order logic and the gamma graphs for modal and higher-order logics, among others. As a logical syntax, EGs are two-dimensional graphs, or diagrams, in contrast to the linear algebraic notations. Peirce's theory of EGs is not only a theory of logical (...)
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  19.  28
    Sequent Calculi for Global Modal Consequence Relations.Minghui Ma & Jinsheng Chen - 2019 - Studia Logica 107 (4):613-637.
    The global consequence relation of a normal modal logic \ is formulated as a global sequent calculus which extends the local sequent theory of \ with global sequent rules. All global sequent calculi of normal modal logics admits global cut elimination. This property is utilized to show that decidability is preserved from the local to global sequent theories of any normal modal logic over \. The preservation of Craig interpolation property from local to global sequent theories of any normal modal (...)
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  20.  71
    Toward Model-Theoretic Modal Logics.Minghui Ma - 2010 - Frontiers of Philosophy in China 5 (2):294-311.
    Adding certain cardinality quantifiers into first-order language will give substantially more expressive languages. Thus, many mathematical concepts beyond first-order logic can be handled. Since basic modal logic can be seen as the bisimular invariant fragment of first-order logic on the level of models, it has no ability to handle modally these mathematical concepts beyond first-order logic. By adding modalities regarding the cardinalities of successor states, we can, in principle, investigate modal logics of all cardinalities. Thus ways of exploring model-theoretic logics (...)
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