14 found
Order:
  1.  17
    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.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  2.  4
    A Deterministic Weakening of Belnap–Dunn Logic.Minghui Ma & Yuanlei Lin - forthcoming - Studia Logica:1-30.
    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 (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  3.  11
    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 (...)
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  4.  6
    Peirce’s Calculi for Classical Propositional Logic.Minghui Ma & Ahti-Veikko Pietarinen - forthcoming - Review of Symbolic Logic:1-32.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  5.  10
    Sequent Calculi for Global Modal Consequence Relations.Minghui Ma & Jinsheng Chen - forthcoming - Studia Logica:1-25.
    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 (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  6.  2
    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 (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  7.  10
    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 (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  8.  5
    A Three-Valued Fregean Quantification Logic.Minghui Ma & Yuanlei Lin - forthcoming - Journal of Philosophical Logic:1-15.
    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.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  9.  1
    Countably Many Weakenings of Belnap–Dunn Logic.Minghui Ma & Yuanlei Lin - forthcoming - Studia Logica:1-36.
    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 (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  10.  44
    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 (...)
    Direct download (10 more)  
     
    Export citation  
     
    Bookmark  
  11.  5
    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 (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  12.  1
    Labelled Tableau Systems for Some Subintuitionistic Logics.Minghui Ma - forthcoming - Logica Universalis:1-16.
    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.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  13.  7
    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.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  14.  1
    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.
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark