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Title: Decidability of finite satisfiability of two-variable first-order logic with counting and local navigation in unordered unranked trees
Author: Guskov, Yegor
ISNI:       0000 0005 0289 7496
Awarding Body: University of Manchester
Current Institution: University of Manchester
Date of Award: 2018
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First-order logic is a widely used relational language of reasoning. Due to the fact that it is algorithmically impossible to determine whether a given sentence of first-order logic is valid or not, various restrictions of first-order logic have been devised to obtain languages that are less expressive but can be reasoned about by computers more easily. One of such prominent fragments of first-order logic is the two-variable frag- ment. Not only is it possible to check the validity of the sentences of this logic in a bounded amount of time, it is also the case that adding various useful reason- ing capabilities to two-variable first-order logic often preserves the time-bounded validity check. This thesis addresses the problem of the complexity of decidability of var- ious extensions of two-variable first-order logic on a broad scale by offering a systematic overview and comparison of the available results in the field. In addition to that the thesis gives the proof of decidability of the extension of two-variable first-order logic with counting quantifiers and the relation that models parent/child relations in a tree graph. The NEXPTIME upper complexity bound is established for the problem of finite satisfiability of this logic.
Supervisor: Pratt-Hartmann, Ian Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available