Some Sahlqvist Completeness Results for Coalgebraic Logics
نویسندگان
چکیده
This paper presents a first step towards completeness-viacanonicity results for coalgebraic modal logics. Specifically, we consider the relationship between classes of coalgebras for ω-accessible endofunctors and logics defined by Sahlqvist-like frame conditions. Our strategy is based on conjoining two well-known approaches: we represent accessible functors as (equational) quotients of polynomial functors and then use canonicity results for boolean algebras with operators to transport completeness to the coalgebraic setting.
منابع مشابه
Completeness-via-canonicity for coalgebraic logics
This thesis aims to provide a suite of techniques to generate completeness results for coalgebraic logics with axioms of arbitrary rank. We have chosen to investigate the possibility to generalize what is arguably one of the most successful methods to prove completeness results in ‘classical’ modal logic, namely completeness-via-canonicity. This technique is particularly well-suited to a coalge...
متن کاملSahlqvist Theorems for Precontact Logics
Precontact logics are propositional modal logics that have been recently considered in order to obtain decidable fragments of the region-based theories of space introduced by De Laguna and Whitehead. We give the definition of Sahlqvist formulas to this regionbased setting and we prove correspondence and canonicity results. Together, these results give rise to a completeness result for precontac...
متن کاملOn the Fusion of Coalgebraic Logics
Fusion is arguably the simplest way to combine modal logics. For normal modal logics with Kripke semantics, many properties such as completeness and decidability are known to transfer from the component logics to their fusion. In this paper we investigate to what extent these results can be generalised to the case of arbitrary coalgebraic logics. Our main result generalises a construction of Kr...
متن کاملHybrid logics with Sahlqvist axioms
We show that every extension of the basic hybrid logic with modal Sahlqvist axioms is complete. As a corollary of our approach, we also obtain the Beth property for a large class of hybrid logics. Finally, we show that the new completeness result cannot be combined with the existing general completeness result for pure axioms.
متن کاملMonotonic Modal Logics
Monotonic modal logics form a generalisation of normal modal logics in which the additivity of the diamond modality has been weakened to monotonicity: 3p∨3q → 3(p∨q). This generalisation means that Kripke structures no longer form an adequate semantics. Instead monotonic modal logics are interpreted over monotonic neighbourhood structures, that is, neighbourhood structures where the neighbourho...
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 2013