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Positive fragments of coalgebraic logics

2015
*
Logical Methods in Computer Science
*

*Positive*modal

*logic*was introduced in an influential 1995 paper

*of*Dunn as the

*positive*

*fragment*

*of*standard modal

*logic*. ... In this paper, we provide a

*coalgebraic*analysis

*of*this theorem, which not only gives a conceptual proof based on duality theory, but also generalizes Dunn's result from Kripke frames to

*coalgebras*for ...

*POSITIVE*

*FRAGMENTS*

*OF*

*COALGEBRAIC*

*LOGICS*9 Remark 2.7. Alg(L ′ ) is the category

*of*

*positive*modal algebras

*of*Dunn [23] . We shall later see in Corollary 5.17 that it is isomorphic to Alg(L ′ ). ...

##
###
Positive Fragments of Coalgebraic Logics
[chapter]

2013
*
Lecture Notes in Computer Science
*

*Positive*modal

*logic*was introduced in an influential 1995 paper

*of*Dunn as the

*positive*

*fragment*

*of*standard modal

*logic*. ... To see the relevance

*of*a presentation result specific to monotone operations, observe that in the example

*of*

*positive*modal

*logic*it is indeed the case that both and ♦ are monotone. ...

*POSITIVE*

*FRAGMENTS*

*OF*

*COALGEBRAIC*

*LOGICS*9 Remark 2.7. Alg(L ′ ) is the category

*of*

*positive*modal algebras

*of*Dunn [23] . We shall later see in Corollary 5.17 that it is isomorphic to Alg(L ′ ). ...

##
###
Expressiveness Modulo Bisimilarity: A Coalgebraic Perspective
[chapter]

2014
*
Outstanding Contributions to Logic
*

Keywords modal fixpoint

doi:10.1007/978-3-319-06025-5_2
fatcat:rp3ugq6esbcsbomodsj6mwh7ti
*logic*, bisimulation invariance,*coalgebra*,*coalgebraic*modal*logic*, predicate liftings, monadic second-order*logic*. ... One*of*van Benthem's seminal results is the Bisimulation Theorem characterizing modal*logic*as the bisimulation-invariant*fragment**of*first-order*logic*. ... Acknowledgements The research*of*this author has been made possible by VICI grant 639.073.501*of*the Netherlands Organization for Scientific Research (NWO). ...##
###
An institutional approach to positive coalgebraic logic

2015
*
Journal of Logic and Computation
*

T (L, δ) and (L , δ ) are the (strongly finitary)

doi:10.1093/logcom/exv074
fatcat:knrtahnj7jgybmxayswhkjzaw4
*logics**of*T and T Then L is the*positive**fragment**of*L. ...*fragments**of**coalgebraic**logics*, CALCO2013, arXiv:1402.5922 (2014) Cîrstea06 An institution*of*modal*logics*for*coalgebras*, J. ... Poset-functors and their*coalgebras*T : Poset → Poset locally monotone functor T -*coalgebras*Partially ordered set*of*states X = (X , ≤) Examples -ordered automata: X → X A × 2, with A the (discrete) input ...##
###
Logics Admitting Final Semantics
[chapter]

2002
*
Lecture Notes in Computer Science
*

It is shown that a

doi:10.1007/3-540-45931-6_17
fatcat:ndk5qa4rhzbazg5cb4p5j3l67a
*logic*admits nal semantics i the formulas*of*the*logic*are preserved under coproducts (disjoint unions) and quotients (homomorphic images). ... A*logic*for*coalgebras*is said to admit nal semantics i | up to some technical requirements|all de nable classes contain a fully abstract nal*coalgebra*. ... still can have distinct bisimilar points, and to Falk Bartels for suggesting P ne when looking for a category*of**coalgebras*with a nal but not all cofree*coalgebras*. ...##
###
Subsumption Checking in Conjunctive Coalgebraic Fixpoint Logics
[article]

2014
*
arXiv
*
pre-print

We work in the framework

arXiv:1401.6359v5
fatcat:trxo5hf4a5ec7bk7smprdgwa5y
*of**coalgebraic**logic*as a unifying semantic setting. ... Most notably we find tractable*fragments**of*game*logic*and the alternating-time mu-calculus. ... Catesbeiana for unsolicited remarks regarding the absence*of*unsatisfiable formulas in EL. ...##
###
Model Checking Linear Coalgebraic Temporal Logics: An Automata-Theoretic Approach
[chapter]

2011
*
Lecture Notes in Computer Science
*

We then consider linear

doi:10.1007/978-3-642-22944-2_10
fatcat:huuv42pksjantav2zxy5bhesbe
*coalgebraic*temporal*logics*interpreted over non-deterministic*coalgebras*, and show how to reduce the model checking problem for such*logics*to the problem*of*deciding the winner ... We extend the theory*of*maximal traces*of*pointed nondeterministic*coalgebras*by providing an automata-based characterisation*of*the set*of*maximal traces for finite such*coalgebras*. ... Such*logics*arise as certain*fragments**of*the path-based*coalgebraic*temporal*logics*defined in [2] , and are interpreted over*coalgebras**of*type P + •F . ...##
###
Flat Coalgebraic Fixed Point Logics
[chapter]

2010
*
Lecture Notes in Computer Science
*

Extending this notion to the generic semantic framework

doi:10.1007/978-3-642-15375-4_36
fatcat:j7oactbfsrdp5eogwwtsmepsay
*of**coalgebraic**logic*enables covering a wide range*of**logics*beyond the standard mu-calculus including, e.g., flat*fragments**of*the graded mu-calculus ... We give a generic proof*of*completeness*of*the Kozen-Park axiomatization for such flat*coalgebraic*fixpoint*logics*. ... Flat*Coalgebraic*Fixed Point*Logics*We briefly recall the generic framework*of**coalgebraic*modal*logic*[21, 28] , and define its extension with flat fixed point operators, a*fragment**of*the*coalgebraic*...##
###
Modular Games for Coalgebraic Fixed Point Logics

2008
*
Electronical Notes in Theoretical Computer Science
*

The results concerning the implicit negation and the alternation-free

doi:10.1016/j.entcs.2008.05.020
fatcat:d27lk7nsp5es3esonyd2j2aflm
*fragments**of*our*logics*make use*of*the notion*of*an S-modality (*of*some finite arity), with S a syntax constructor with an associated ...*Coalgebraic*fixed point*logics*were first considered in the work*of*Venema [21] , where a finitary version*of*the*coalgebraic**logic**of*Moss [14] was used as the underlying modal language. ... Macros As in the propositional μ-calculus, one can distinguish*fragments**of*our*coalgebraic*fixed point*logics*that have desirable properties, for example the independent fixed point*fragment*IμL S (V) ...##
###
Coalgebraic Predicate Logic
[chapter]

2012
*
Lecture Notes in Computer Science
*

We study the expressive power

doi:10.1007/978-3-642-31585-5_29
fatcat:qtsjcom6jrfq7kfdiof634peou
*of*our language, contrasting it with both*coalgebraic*modal*logic*and existing first-order proposals for special classes*of*Set-*coalgebras*(apart for relational structures ... We propose a generalization*of*first-order*logic*originating in a neglected work by C.C. ... Section 4 gives both syntactic and semantic characterizations*of**coalgebraic*modal*logic*as a*fragment**of*CPL. ...##
###
Structure and Power: an emerging landscape
[article]

2022
*
arXiv
*
pre-print

induced by (i) the quantifier rank

arXiv:2206.07393v3
fatcat:nxdo3tdi5zdexngwqpgysyvamu
*fragments*, (ii) the restriction*of*this*fragment*to the existential*positive*part, and (iii) the extension with counting quantifiers; and the combinatorial parameter ... One basic instance*of*this scheme allows us to recover, in a purely structural, syntax-free way: the Ehrenfeucht-Fraisse~game; the quantifier rank*fragments**of*first-order*logic*; the equivalences on structures ... considered: full modal*logic**of*depth ≤ k, the diamond-only*positive**fragment*, and graded modal*logic*[19] for the counting case. • The*coalgebra*number in this case recovers the property*of*being a ...##
###
Coalgebraic Correspondence Theory
[chapter]

2010
*
Lecture Notes in Computer Science
*

invariant

doi:10.1007/978-3-642-12032-9_23
fatcat:iiney5jh7fgizoggbafg6mxbra
*fragment**of*first-order*logic*. ... We lay the foundations*of*a first-order correspondence theory for*coalgebraic**logics*that makes the transition structure explicit in the first-order modelling. ... Catesbeiana for suggesting the use*of*⊥. ...##
###
Monadic Second-Order Logic and Bisimulation Invariance for Coalgebras

2015
*
2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science
*

Similar to well-known results for monadic second-order

doi:10.1109/lics.2015.41
dblp:conf/lics/EnqvistSV15
fatcat:hvvangchijci7bkfcknj2me2c4
*logic*over trees, we provide a translation*of*this*logic*into a class*of*automata, relative to the class*of*T-*coalgebras*that admit a tree-like supporting ... We then consider invariance under behavioral equivalence*of*MSO T -formulas; more in particular, we investigate whether the*coalgebraic*µ-calculus is the bisimulation-invariant*fragment**of*MSO T . ... Introduction*Logic*, automata and*coalgebra*The aim*of*this paper is to strengthen the link between the areas*of**logic*, automata and*coalgebra*. ...##
###
Monadic Second-Order Logic and Bisimulation Invariance for Coalgebras
[article]

2015
*
arXiv
*
pre-print

Similar to well-known results for monadic second-order

arXiv:1501.07215v1
fatcat:ib3bdpazubdttpmmtrm55exv6y
*logic*over trees, we provide a translation*of*this*logic*into a class*of*automata, relative to the class*of**coalgebras*that admit a tree-like supporting ... We then consider invariance under behavioral equivalence*of*formulas; more in particular, we investigate whether the*coalgebraic*mu-calculus is the bisimulation-invariant*fragment**of*monadic second-order ... Introduction*Logic*, automata and*coalgebra*The aim*of*this paper is to strengthen the link between the areas*of**logic*, automata and*coalgebra*. ...##
###
Coalgebraic Expressions

2009
*
Fixed Points in Computer Science
*

There is an associated complete equational

dblp:conf/fics/Myers09
fatcat:odizieeuw5hfxnpwlrqsbkq2oq
*logic*, analogous to Kleene algebra, which may now be seen as an equational presentation*of*a*fragment**of*the*coalgebraic*µ-calculus. ... These expressions include the regular expressions, the free Kleene algebra with tests and*fragments**of*CCS and Linear Temporal*Logic*. ... The equational*logic*≡ K may be understood as an interesting equational presentation*of*a*fragment**of*the*coalgebraic*µ-calculus. ...
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