Zobrazeno 1 - 10
of 62
pro vyhledávání: '"Litak, Tadeusz"'
Autor:
Visser, Albert, Litak, Tadeusz
We study the principle phi implies box phi, known as `Strength' or `the Completeness Principle', over the constructive version of L\"ob's Logic. We consider this principle both for the modal language with the necessity operator and for the modal lang
Externí odkaz:
http://arxiv.org/abs/2404.11969
Autor:
Litak, Tadeusz
In 1984, Wim Ruitenburg published a surprising result about periodic sequences in intuitionistic propositional calculus (IPC). The property established by Ruitenburg naturally generalizes local finiteness (intuitionistic logic is not locally finite,
Externí odkaz:
http://arxiv.org/abs/2402.01840
Heyting-Lewis Logic is the extension of intuitionistic propositional logic with a strict implication connective that satisfies the constructive counterparts of axioms for strict implication provable in classical modal logics. Variants of this logic a
Externí odkaz:
http://arxiv.org/abs/2105.01873
Autor:
Litak, Tadeusz, Visser, Albert
Our paper is the first study of what one might call "reverse mathematics of explicit fixpoints". We study two methods of constructing such fixpoints for formulas whose principal connective is the intuitionistic Lewis arrow. Our main motivation comes
Externí odkaz:
http://arxiv.org/abs/1905.09450
Autor:
Holliday, Wesley H., Litak, Tadeusz
Publikováno v:
The Review of Symbolic Logic 12 (2019) 487-535
In this paper, we tell a story about incompleteness in modal logic. The story weaves together a paper of van Benthem, `Syntactic aspects of modal incompleteness theorems,' and a longstanding open question: whether every normal modal logic can be char
Externí odkaz:
http://arxiv.org/abs/1809.07542
Autor:
Litak, Tadeusz
Publikováno v:
Bulletin of the Section of Logic, vol. 33(2), pp. 81-86, 2004
I investigate the superintuitionistic analogue of the modal logic of chequered subsets of $\mathbb{R}^\infty$ introduced by van Benthem et al. It is observed that this logic possesses the disjunction property, contains the Scott axiom, fails to conta
Externí odkaz:
http://arxiv.org/abs/1808.06393
Autor:
Litak, Tadeusz
Publikováno v:
Reports on Mathematical Logic 36, pp. 131-141, 2002
This paper generalizes the 1977 paper of V.B. Shehtman, which constructed the first Kripke incomplete intermediate logic, by presenting a continuum of such logics. This version fixes an error in my simplified proof of incompleteness of Shehtman's ori
Externí odkaz:
http://arxiv.org/abs/1808.06284
Autor:
Jipsen, Peter, Litak, Tadeusz
We overview the logic of Bunched Implications (BI) and Separation Logic (SL) from a perspective inspired by Hiroakira Ono's algebraic approach to substructural logics. We propose generalized BI algebras (GBI-algebras) as a common framework for algebr
Externí odkaz:
http://arxiv.org/abs/1709.07063
Autor:
Litak, Tadeusz
I overview the work of the Tbilisi school on intuitionistic modal logics of well-founded/scattered structures and its connections with contemporary theoretical computer science. Fixed-point theorems and their consequences are of particular interest.<
Externí odkaz:
http://arxiv.org/abs/1708.05607
Autor:
Litak, Tadeusz, Visser, Albert
C. I. Lewis invented modern modal logic as a theory of "strict implication". Over the classical propositional calculus one can as well work with the unary box connective. Intuitionistically, however, the strict implication has greater expressive powe
Externí odkaz:
http://arxiv.org/abs/1708.02143