29 citations · 84 across the 12 of their papers we have counts for
13 papers
Relational Semantics for Flat Heyting-Lewis Logic
Jim de Groot, Tadeusz Litak
We introduce relational semantics for "flat Heyting-Lewis logic" HLC-flat. This logic arises as the extension of intuitionistic logic with a Lewis-style strict implication modality…
Bounded Inquisitive Logics: Sequent Calculi and Schematic Validity
Tadeusz Litak, Katsuhiko Sano
Propositional inquisitive logic is the limit of its -bounded approximations. In the predicate setting, however, this does not hold anymore, as discovered by Ciardelli and Grille…
Gödel-McKinsey-Tarski and (not quite) Blok-Esakia for Heyting-Lewis Implication
Jim de Groot, Tadeusz Litak, Dirk Pattinson
Heyting-Lewis Logic is the extension of intuitionistic propositional logic with a strict implication connective that satisfies the constructive counterparts of axioms for strict im…
Lewisian Fixed Points I: Two Incomparable Constructions
Tadeusz Litak, Albert Visser
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 co…
Complete Additivity and Modal Incompleteness
Wesley H. Holliday, Tadeusz Litak
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 lo…
Some notes on the superintuitionistic logic of chequered subsets of
Tadeusz Litak
I investigate the superintuitionistic analogue of the modal logic of chequered subsets of introduced by van Benthem et al. It is observed that this logic posses…
A continuum of incomplete intermediate logics
Tadeusz Litak
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 fix…
An Algebraic Glimpse at Bunched Implications and Separation Logic
Peter Jipsen, Tadeusz Litak
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 g…
Constructive Modalities with Provability Smack
Tadeusz Litak
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. Fi…
Lewis meets Brouwer: constructive strict implication
Tadeusz Litak, Albert Visser
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. Intuition…
Model Theory and Proof Theory of Coalgebraic Predicate Logic
Tadeusz Litak, Dirk Pattinson, Katsuhiko Sano +1
We propose a generalization of first-order logic originating in a neglected work by C.C. Chang: a natural and generic correspondence language for any types of structures which can…
Guard Your Daggers and Traces: Properties of Guarded (Co-)recursion
Stefan Milius, Tadeusz Litak
Motivated by the recent interest in models of guarded (co-)recursion, we study their equational properties. We formulate axioms for guarded fixpoint operators generalizing the axio…
Guard Your Daggers and Traces: On The Equational Properties of Guarded (Co-)recursion
Stefan Milius, Tadeusz Litak
Motivated by the recent interest in models of guarded (co-)recursion we study its equational properties. We formulate axioms for guarded fixpoint operators generalizing the axioms…