Free Modal Algebras: A Coalgebraic Perspective
نویسندگان
چکیده
In this paper we discuss a uniform method for constructing free modal and distributive modal algebras. This method draws on works by (Abramsky 2005) and (Ghilardi 1995). We revisit the theory of normal forms for modal logic and derive a normal form representation for positive modal logic. We also show that every finitely generated free modal and distributive modal algebra axiomatised by equations of rank 1 is a reduct of a temporal algebra.
منابع مشابه
Algebraic Semantics for Coalgebraic Logics
With coalgebras usually being defined in terms of an endofunctor T on sets, this paper shows that modal logics for T -coalgebras can be naturally described as functors L on boolean algebras. Building on this idea, we study soundness, completeness and expressiveness of coalgebraic logics from the perspective of duality theory. That is, given a logic L for coalgebras of an endofunctor T , we cons...
متن کاملA New Coalgebraic Semantics for Positive Modal Logic
Positive Modal Logic is the restriction of the modal local consequence relation defined by the class of all Kripke models to the propositional negation-free modal language. The class of positive modal algebras is the one canonically associated with PML according to the theory of Abstract Algebraic Logic. In [4], a Priestley-style duality is established between the category of positive modal alg...
متن کاملA coalgebraic view on positive modal logic
Positive Modal Logic is the restriction of the modal local consequence relation defined by the class of all Kripke models to the propositional negation-free modal language. The class of positive modal algebras is the one canonically associated with PML according to the theory of the algebrization of logics [12]. A Priestley-style duality is established between the category of positive modal alg...
متن کاملSome Sahlqvist Completeness Results for Coalgebraic Logics
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 polynomi...
متن کاملAlgebraic-Coalgebraic Specification in Co Casl
We introduce CoCasl as a light-weight but expressive coalgebraic extension of the algebraic specification language Casl. CoCasl allows the nested combination of algebraic datatypes and coalgebraic process types. Moreover, it provides syntactic sugar for an observer-indexed modal logic that allows e.g. expressing fairness properties. This logic includes a generic definition of modal operators fo...
متن کامل