Line-Based Affine Reasoning in Euclidean Plane

Line-Based Affine Reasoning in Euclidean Plane

We consider the binary relations of parallelism and convergence between lines in a 2-dimensional affinespace. Associating with parallelism and convergence the binary predicates P and C and the modal connectives [ P] and [C], we consider a first-order theory based on these predicates and a modal logi...

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Bibliographische Detailangaben
Hauptverfasser: Balbiani, Philippe, Tinchev, Tinko
Format: Tagungsbericht
Sprache:eng
Schlagworte:
Applied sciences
Artificial intelligence
Computer Science
Computer science
control theory
systems
Euclidean Plane
Exact sciences and technology
Kripke Model
Learning and adaptive systems
Logic in Computer Science
Logical, boolean and switching functions
Membership Problem
Modal Logic
Propositional Variable
Theoretical computing
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Beschreibung
Zusammenfassung:We consider the binary relations of parallelism and convergence between lines in a 2-dimensional affinespace. Associating with parallelism and convergence the binary predicates P and C and the modal connectives [ P] and [C], we consider a first-order theory based on these predicates and a modal logic based on these modal connectives. We investigate the axiomatization/completeness and the decidability/complexity of this first-order theory and this modal logic.
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-540-30227-8_40