Algorithmic canonicity and correspondence for (non-distributive) lattice-based modal logic
نویسندگان
چکیده
09h00 09h45 Zurab Janelidze Algebraic importance of “modus ponens” 09h50 10h20 Gareth Boxall NIP (Not the Independence Property) 10h25 10h55 James Gray Algebraic exponentiation 11h00 11h15 Tea/coffee Mathematics Tea Room 11h15 12h15 Alessandra Palmigiano Groupoid quantales beyond the étale setting 12h20 12h50 Willem Conradie Algorithmic canonicity and correspondence for (non-distributive) lattice-based modal logic 12h55 14h25 Lunch Stellenbosch Botanical Garden 14h30 15h15 James Raftery Idempotent residuated structures and finiteness conditions 15h20 15h50 Tamar Janelidze Relative Goursat categories 15h55 16h25 Clint van Alten Representable Ideal-determined Varieties 16h30 16h45 Tea/Coffee Mathematics Tea Room 16h45 17h15 Marcel Wild Enumerating all models of a Horn formula, e.g. all closed sets of a closure system 17h20 17h50 George Janelidze What shall be 2-dimensional topology of first order logic?
منابع مشابه
Algorithmic Correspondence and Canonicity for Possibility Semantics (Abstract)
Unified Correspondence. Correspondence and completeness theory have a long history in modal logic, and they are referred to as the “three pillars of wisdom supporting the edifice of modal logic” [22, page 331] together with duality theory. Dating back to [20,21], the Sahlqvist theorem gives a syntactic definition of a class of modal formulas, the Sahlqvist class, each member of which defines an...
متن کاملConstructive Canonicity for Lattice-Based Fixed Point Logics
The present contribution lies at the crossroads of at least three active lines of research in nonclassical logics: the one investigating the semantic and proof-theoretic environment of fixed point expansions of logics algebraically captured by varieties of (distributive) lattice expansions [1, 19, 24, 2, 16]; the one investigating constructive canonicity for intuitionistic and substructural log...
متن کاملAlgebraic Canonicity in Non-Classical Logics
This thesis is a study of the notion of canonicity (as is understood e.g. in modal logic) from an algebraic viewpoint. The main conceptual contribution of this thesis is a better understanding of the connection between the Jónsson-style canonicity proof and the canonicity-via-correspondence. The main results of this thesis include an ALBA-aided Jónsson-style canonicity proof for inductive inequ...
متن کاملAlgorithmic correspondence and canonicity for distributive modal logic
We define the algorithm ALBA for the language of the same distributive modal logic (DML) for which a Sahlqvist theorem was proved by Gehrke, Nagahashi, and Venema. Successful executions of ALBA compute the local first-order correspondents of input DML inequalities, and also guarantee their canonicity. The class of inequalities on which ALBA is successful is strictly larger than the newly introd...
متن کاملCanonicity and Relativized Canonicity via Pseudo-Correspondence: an Application of ALBA
We generalize Venema’s result on the canonicity of the additivity of positive terms, from classical modal logic to a vast class of logics the algebraic semantics of which is given by varieties of normal distributive lattice expansions (normal DLEs), aka ‘distributive lattices with operators’. We provide two contrasting proofs for this result: the first is along the lines of Venema’s pseudocorre...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010