Expressiveness and completeness of an interval tense logic.

Venema, Yde

doi:10.1305/ndjfl/1093635589

Cited by 125 publications

(96 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Projection-based spatial logics (most notably, Compass Logic [13]) are two-dimensional modal logics whose accessibility relations allow one to move along one of the two coordinates while keeping the other coordinate constant. On the one hand, Cone Logic inherits from projectionbased modal logics some of their desirable features.…”

Section: Ll(p) Lr(p) Ul(p) and Ur(p) The Open Lower-left Lower-rimentioning

confidence: 99%

A Decidable Spatial Logic with Cone-Shaped Cardinal Directions

Montanari

Puppis

Sala

2009

Computer Science Logic

View full text Add to dashboard Cite

Section: Ll(p) Lr(p) Ul(p) and Ur(p) The Open Lower-left Lower-rimentioning

confidence: 99%

A Decidable Spatial Logic with Cone-Shaped Cardinal Directions

Montanari

Puppis

Sala

2009

Computer Science Logic

View full text Add to dashboard Cite

“…Examples include Burgess [6], Zanardo [45] for branching-time temporal logics, Kuhn [22] and Venema [37,38,39,42,43] for many-dimensional modal logics (of intervals), and Gabbay & Hodkinson [11], de Rijke [28], Roorda [30]. There is an originally independent Bulgarian line of papers: Passy-Tinchev [26], Gargov & Goranko [12], Gargov, Passy & Tinchev [13], Goranko [17] where similar rules are used in a context of enriched modal formalisms.…”

Section: (Ir)mentioning

confidence: 99%

Derivation rules as anti-axioms in modal logic

Venema¹

1993

J. symb. log.

Self Cite

View full text Add to dashboard Cite

Abstract.We discuss a 'negative' way of defining frame classes in (multi-)modal logic, and address the question whether these classes can be axiomatized by derivation rules, the 'non-ξ rules', styled after Gabbay's Irreflexivity Rule. The main result of this paper is a meta-theorem on completeness, of the following kind: If Λ is a derivation system having a set of axioms that are special Sahlqvist formulas, and Λ + is the extension of Λ with a set of non-ξ rules, then Λ + is strongly sound and complete with respect to the class of frames determined by the axioms and the rules.

show abstract

“…Two other applications of two-variable logic on two-dimensional structures arises from its close connection to compass logic and interval temporal logic. In compass logic, two-dimensional temporal operators allow for moving north, south, east and west in the two-dimensional plane [Ven90]. In interval temporal logic operators like 'after', 'during' and 'begins' allow for moving along intervals [HS91].…”

Section: Transfer Of Techniquesmentioning

confidence: 99%

Small Dynamic Complexity Classes

Zeume

2017

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Everything changes and nothing stands still. -Heraclitus (quoted by Platon in Cratylus) PrefaceOn the first few days of my PhD studies in the summer of 2009, my adviser Thomas Schwentick introduced me to dynamic complexity. Very recently Wouter Gelade, Marcel Marquardt and Thomas had obtained a very nice characterization of regular languages in terms of dynamic complexity, and also a lower bound for the dynamic complexity of the alternating reachability problem. Many interesting problems in this area seemed to wait for a solution; and so I started to try to prove a lower bound for reachability. I was not successful. After two (at the end frustrating) months, I abandoned this project.In the following two and a half years I almost forgot about dynamic complexity. Decidability issues for the two-variable fragment of first-order logic had turned out to be a much more accessible and fruitful field. Thomas and I had obtained several results, and a PhD in this field seemed not to be too far away. This was the moment when Thomas asked whether I would be interested in applying for funds from the DFG. If successful, such funding could relieve me from my teaching obligations.We decided to have a second, deeper look into dynamic complexity, and to apply for funds for doing an extensive study of the power of logics in dynamic settings. At that time, the decision to spend more time on dynamic complexity was not easy for me. I was in the third year of my PhD and already had results and further ideas for two-variable logics; and it was not clear whether an application for funding would be successful. On the other hand, now I had more experience, which might turn out to be helpful to attack the very same problems that I had tried to solve at the beginning of my PhD. I do not regret the decision.With the thesis at hand I want to document the progress in dynamic complexity that we have made in the last two and a half years. The focus of this thesis is on small dynamic descriptive complexity classes, in particular on lower bound methods for them. A short summary of results on decidability issues for two-variable logic is presented at the end of the thesis.

show abstract

Expressiveness and completeness of an interval tense logic.

Cited by 125 publications

References 3 publications

A Decidable Spatial Logic with Cone-Shaped Cardinal Directions

A Decidable Spatial Logic with Cone-Shaped Cardinal Directions

Derivation rules as anti-axioms in modal logic

Small Dynamic Complexity Classes

Contact Info

Product

Resources

About