On Logics and Homomorphism Closure

Predicate logic is the premier choice for specifying classes of relational structures. Homomorphisms are key to describing correspondences between relational structures. Questions concerning the interdependencies between these two means of characterizing (classes of) structures are of fundamental in...

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Vydáno v:Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science s. 1 - 13
Hlavní autoři: Bodirsky, Manuel, Feller, Thomas, Knauer, Simon, Rudolph, Sebastian
Médium: Konferenční příspěvek
Jazyk:angličtina
Vydáno: IEEE 29.06.2021
Témata:
Analytical models
Complexity theory
Computational modeling
Computer science
Fasteners
Inspection
Syntactics
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Shrnutí:Predicate logic is the premier choice for specifying classes of relational structures. Homomorphisms are key to describing correspondences between relational structures. Questions concerning the interdependencies between these two means of characterizing (classes of) structures are of fundamental interest and can be highly non-trivial to answer. We investigate several problems regarding the homomorphism closure (homclosure) of the class of all (finite or arbitrary) models of logical sentences: membership of structures in a sentence's homclosure; sentence homclosedness; homclosure characterizability in a logic; normal forms for homclosed sentences in certain logics. For a wide variety of fragments of first- and second-order predicate logic, we clarify these problems' computational properties.
DOI:10.1109/LICS52264.2021.9470511