5 found
Order:
  1.  26
    Definite Formulae, Negation-as-Failure, and the Base-Extension Semantics of Intuitionistic Propositional Logic.Alexander V. Gheorghiu & David J. Pym - 2023 - Bulletin of the Section of Logic 52 (2):239-266.
    Proof-theoretic semantics (P-tS) is the paradigm of semantics in which meaning in logic is based on proof (as opposed to truth). A particular instance of P-tS for intuitionistic propositional logic (IPL) is its base-extension semantics (B-eS). This semantics is given by a relation called support, explaining the meaning of the logical constants, which is parameterized by systems of rules called bases that provide the semantics of atomic propositions. In this paper, we interpret bases as collections of definite formulae and use (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  2.  18
    Reductive Logic, Proof-Search, and Coalgebra: A Perspective from Resource Semantics.Alexander V. Gheorghiu, Simon Docherty & David J. Pym - 2023 - In Alessandra Palmigiano & Mehrnoosh Sadrzadeh (eds.), Samson Abramsky on Logic and Structure in Computer Science and Beyond. Springer Verlag. pp. 833-875.
    The reductive, as opposed to deductive, view of logic is the form of logic that is, perhaps, most widely employed in practical reasoning. In particular, it is the basis of logic programming. Here, building on the idea of uniform proof in reductive logic, we give a treatment of logic programming for BI, the logic of bunched implications, giving both operational and denotational semantics, together with soundness and completeness theorems, all couched in terms of the resource interpretation of BI’s semantics. We (...)
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark   2 citations  
  3.  4
    From Proof-Theoretic Validity to Base-Extension Semantics for Intuitionistic Propositional Logic.Alexander V. Gheorghiu & David J. Pym - forthcoming - Studia Logica:1-33.
    Proof-theoretic semantics (P-tS) is the approach to meaning in logic based on _proof_ (as opposed to truth). There are two major approaches to P-tS: proof-theoretic validity (P-tV) and base-extension semantics (B-eS). The former is a semantics of arguments, and the latter is a semantics of logical constants. This paper demonstrates that the B-eS for _intuitionistic propositional logic_ (IPL) encapsulates the declarative content of a version of P-tV based on the elimination rules. This explicates how the B-eS for IPL works, and (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  4.  28
    Semantical Analysis of the Logic of Bunched Implications.Alexander V. Gheorghiu & David J. Pym - 2023 - Studia Logica 111 (4):525-571.
    We give a novel approach to proving soundness and completeness for a logic (henceforth: the object-logic) that bypasses truth-in-a-model to work directly with validity. Instead of working with specific worlds in specific models, we reason with eigenworlds (i.e., generic representatives of worlds) in an arbitrary model. This reasoning is captured by a sequent calculus for a _meta_-logic (in this case, first-order classical logic) expressive enough to capture the semantics of the object-logic. Essentially, one has a calculus of validity for the (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  5.  2
    Proof-theoretic Semantics for Intuitionistic Multiplicative Linear Logic.Alexander V. Gheorghiu, Tao Gu & David J. Pym - forthcoming - Studia Logica:1-61.
    Proof-theoretic semantics (P-tS) is an innovative approach to grounding logical meaning in terms of proofs rather than traditional truth-conditional semantics. The point is not that one provides a proof system, but rather that one articulates meaning in terms of proofs and provability. To elucidate this paradigm shift, we commence with an introduction that contrasts the fundamental tenets of P-tS with the more prevalent model-theoretic approach to semantics. The contribution of this paper is a P-tS for a substructural logic, intuitionistic multiplicative (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark