Logic Journal of the IGPL

ISSN: 0945-9103

11 found

View year:

  1.  8
    The limitless first incompleteness theorem.Yong Cheng - 2025 - Logic Journal of the IGPL 33 (3).
    This work is motivated by the problem of finding the limit of the applicability of the first incompleteness theorem ($\textsf{G1}$). A natural question is, can we find a minimal theory for which $\textsf{G1}$ holds? We examine the Turing degree structure of recursively enumerable (RE) theories for which $\textsf{G1}$ holds and the interpretation degree structure of RE theories weaker than the theory $\textbf{R}$ with respect to interpretation for which $\textsf{G1}$ holds. We answer all questions that we posed in [2], and prove (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  2.  3
    Computable operators on left–c.e. reals and their continuity properties.M. Faizrahmanov - 2025 - Logic Journal of the IGPL 33 (3).
    We consider two computability notions for functions mapping all left-c.e. reals to left-c.e. reals, namely functions computable in the Banach–Mazur and Markov senses. We show that any total Banach–Mazur computable function is also Markov computable, but this is no longer true for partial functions. We also prove a sufficient condition for the almost continuity on the left of Banach–Mazur computable functions, from which it follows that Markov computable functions that are total or whose domains are sets of left-c.e. reals common (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  3.  30
    Simple sequent systems for the modal logics K,D,T, and S4.Rea Golan - 2025 - Logic Journal of the IGPL 33 (3):1-24.
    Proof theorists have long been struggling to provide simple accounts of various modal logics. Drawing on the recent literature on metainferences, I develop in the present paper a novel approach to this challenge: regular sequent systems augmented with natural deduction-like rules for assuming and discharging sequents. Based on this approach, I introduce an elegant calculus for the modal logic S4⁠. Various discharging conditions on assumptions are shown to yield the weaker logics K⁠, D, and ⁠T. The rules in these calculi (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  4.  36
    Symmetric and conflated intuitionistic logics.Norihiro Kamide - 2025 - Logic Journal of the IGPL 33 (2).
    Two new propositional non-classical logics, referred to as symmetric intuitionistic logic (SIL) and conflated intuitionistic logic (CIL), are introduced as indexed and non-indexed Gentzen-style sequent calculi. SIL is regarded as a natural hybrid logic combining intuitionistic and dual-intuitionistic logics, whereas CIL is regarded as a variant of intuitionistic paraconsistent logic with conflation and without paraconsistent negation. The cut-elimination theorems for SIL and CIL are proved. CIL is shown to be conservative over SIL.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  5.  17
    On elementary equivalence of real semigroups of preordered rings.F. Miraglia & Hugo Mariano - 2025 - Logic Journal of the IGPL 33 (2).
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  6.  27
    Undecidability of admissibility in the product of two Alt logics.Philippe Balbiani & Çiğdem Gencer - 2025 - Logic Journal of the IGPL 33 (1):62-73.
    The product of two $\textbf {Alt}$ logics possesses the polynomial product finite model property and its membership problem is $\textbf {coNP}$-complete. Using a reduction from an undecidable domino-tiling problem, we prove that its admissibility problem is undecidable.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  7.  3
    On the number of different variables required to define the n-density or the bounded n-width of Kripke frames with some consequences for Sahlqvist formulae.Petar Iliev - 2025 - Logic Journal of the IGPL 33 (1):95-124.
    We show that both the $n$-density and the bounded $n$-width of Kripke frames can be modally defined not only with natural and well-known Sahlqvist formulae containing a linear number of different propositional variables but also with formulae of polynomial length with a logarithmic number of different propositional variables and then we prove that this exponential decrease in the number of variables leads us outside the class of Sahlqvist formulae.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  8.  25
    Knowledge and ignorance in Belnap–Dunn logic.Daniil Kozhemiachenko & Liubov Vashentseva - 2025 - Logic Journal of the IGPL 33 (1):125-148.
    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 (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  9.  18
    Modal expansions of ririgs.AgustÍn L. Nagy & William J. Zuluaga Botero - 2025 - Logic Journal of the IGPL 33 (1):74-94.
    In this paper, we introduce the variety of $I$-modal ririgs. We characterize the congruence lattice of its members by means of $I$-filters, and we provide a description of $I$-filter generation. We also provide an axiomatic presentation for the variety generated by chains of the subvariety of contractive $I$-modal ririgs. Finally, we introduce a Hilbert-style calculus for a logic with $I$-modal ririgs as an equivalent algebraic semantics and we prove that such a logic has the parametrized local deduction-detachment theorem.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  10.  5
    Labelled proof systems for existential reasoning.Jaime Ramos, João Rasga & Cristina Sernadas - 2025 - Logic Journal of the IGPL 33 (1):173-201.
    Usually in logic, proof systems are defined having in mind proving properties like validity and semantic consequence. It seems worthwhile to address the problem of having proof systems where satisfiability is a primitive notion in the sense that a formal derivation means that a finite set of formulas is satisfiable. Moreover, it would be useful to cover within the same framework as many logics as possible. We consider Kripke semantics where the properties of the constructors are provided by valuation constraints (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  11.  27
    Constructive theories through a modal lens.Matteo Tesi - 2025 - Logic Journal of the IGPL 33 (1):149-172.
    We present a uniform proof-theoretic proof of the Gödel–McKinsey–Tarski embedding for a class of first-order intuitionistic theories. This is achieved by adapting to the case of modal logic the methods of proof analysis in order to convert axioms into rules of inference of a suitable sequent calculus. The soundness and the faithfulness of the embedding are proved by induction on the height of the derivations in the augmented calculi. Finally, we define an extension of the modal system for which the (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
 Previous issues
  
Next issues