scholarly journals Equivalence closure in the two-variable guarded fragment

2015 ◽  
pp. exv075 ◽  
Author(s):  
Emanuel Kieroński ◽  
Ian Pratt-Hartmann ◽  
Lidia Tendera
Keyword(s):  
Guarded Fragment

scholarly journals Querying the Guarded Fragment

2010 ◽  
Author(s):  
Vince Bárány ◽  
Georg Gottlob ◽  
Martin Otto
Keyword(s):  
Guarded Fragment

Querying the Guarded Fragment with Transitivity

2013 ◽  
pp. 287-298 ◽  
Author(s):  
Georg Gottlob ◽  
Andreas Pieris ◽  
Lidia Tendera
Keyword(s):  
Guarded Fragment

scholarly journals Beth Definability for the Guarded Fragment

1999 ◽  
pp. 273-285 ◽  
Author(s):  
Eva Hoogland ◽  
Maarten Marx ◽  
Martin Otto
Keyword(s):  
Beth Definability ◽  
Guarded Fragment

EXPSPACE-Complete Variant of Guarded Fragment with Transitivity

2002 ◽  
pp. 608-619 ◽  
Author(s):  
Emanuel Kieroński
Keyword(s):  
Guarded Fragment

scholarly journals Highly acyclic groups, hypergraph covers, and the guarded fragment

2012 ◽  
Vol 59 (1) ◽  
pp. 1-40 ◽  
Author(s):  
Martin Otto
Keyword(s):  
Guarded Fragment

scholarly journals Undecidable relativizations of algebras of relations

1999 ◽  
Vol 64 (2) ◽  
pp. 747-760 ◽  
Author(s):  
Szabolcs Mikulás ◽  
Maarten Marx
Keyword(s):  
Order Logic ◽  
First Order Logic ◽  
Similarity Type ◽  
First Order ◽  
Equational Theories ◽  
Algebras Of Relations ◽  
Guarded Fragment ◽  
Cylindric Set Algebras

AbstractIn this paper we show that relativized versions of relation set algebras and cylindric set algebras have undecidable equational theories if we include coordinatewise versions of the counting operations into the similarity type. We apply these results to the guarded fragment of first-order logic.

scholarly journals The Triguarded Fragment with Transitivity

10.29007/z359 ◽  
2020 ◽  
Author(s):  
Emanuel Kieronski ◽  
Adam Malinowski
Keyword(s):  
Decision Procedure ◽  
Order Logic ◽  
First Order Logic ◽  
Satisfiability Problem ◽  
First Order ◽  
Free Variables ◽  
Guarded Fragment

The triguarded fragment of first-order logic is an extension of the guarded fragment in which quantification for subformulas with at most two free variables need not be guarded. Thus, it unifies two prominent decidable logics: the guarded fragment and the two-variable fragment. Its satisfiability problem is known to be undecidable in the presence of equality, but becomes decidable when equality is forbidden. We consider an extension of the tri- guarded fragment without equality by transitive relations, allowing them to be used only as guards. We show that the satisfiability problem for the obtained formalism is decidable and 2-ExpTime-complete, that is, it is of the same complexity as for the analogous exten- sion of the classical guarded fragment. In fact, in our satisfiability test we use a decision procedure for the latter as a subroutine. We also show how our approach, consisting in exploiting some existing results on guarded logics, can be used to reprove some known facts, as well as to derive some other new results on triguarded logics.

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