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 |
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| Jazyk: | angličtina |
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IEEE
29.06.2021
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Knauer, Simon Feller, Thomas Rudolph, Sebastian Bodirsky, Manuel |
| Author_xml | – sequence: 1 givenname: Manuel surname: Bodirsky fullname: Bodirsky, Manuel organization: Institut für Algebra TU Dresden – sequence: 2 givenname: Thomas surname: Feller fullname: Feller, Thomas organization: Computational Logic Group TU Dresden – sequence: 3 givenname: Simon surname: Knauer fullname: Knauer, Simon organization: Institut für Algebra TU Dresden – sequence: 4 givenname: Sebastian surname: Rudolph fullname: Rudolph, Sebastian organization: Computational Logic Group TU Dresden |
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| Snippet | Predicate logic is the premier choice for specifying classes of relational structures. Homomorphisms are key to describing correspondences between relational... |
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| SubjectTerms | Analytical models Complexity theory Computational modeling Computer science Fasteners Inspection Syntactics |
| Title | On Logics and Homomorphism Closure |
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