Exploiting Forwardness: Satisfiability and Query-Entailment in Forward Guarded Fragment

Bednarczyk, Bartosz

doi:10.1007/978-3-030-75775-5_13

Cited by 7 publications

(12 citation statements)

References 15 publications

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“…Notice that if ϕ(x) ∈ L affix (n), where x lists all the free variables of ϕ in order (with respect to their indices), then x is an affix of the tuple x 1...n . The logics L pre , L suf , and L inf were studied under the names of ordered [11], fluted [21], and forward [4] fragments. The guarded counterparts G affix of L affix , are defined as the intersection of L affix and the guarded fragment GF [1], i.e.…”

Section: Tuples and Subsequencesmentioning

confidence: 99%

Towards a Model Theory of Ordered Logics: Expressivity and Interpolation (Extended version)

Bednarczyk¹,

Jaakkola²

2022

Preprint

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We consider the family of guarded and unguarded ordered logics, that constitute a recently rediscovered family of decidable fragments of first-order logic (FO), in which the order of quantification of variables coincides with the order in which those variables appear as arguments of predicates. While the complexities of their satisfiability problems are now well-established, their model theory, however, is poorly understood. Our paper aims to provide some insight into it.We start by providing suitable notions of bisimulation for ordered logics. We next employ bisimulations to compare the relative expressive power of ordered logics, and to characterise our logics as bisimulation-invariant fragments of FO à la van Benthem.Afterwards, we study the Craig Interpolation Property (CIP). We refute yet another claim from the infamous work by Purdy, by showing that the fluted and forward fragments do not enjoy CIP. We complement this result by showing that the ordered fragment and the guarded ordered logics enjoy CIP. These positive results rely on novel and quite intricate model constructions, which take full advantage of the "forwardness" of our logics.

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Section: Tuples and Subsequencesmentioning

confidence: 99%

Towards a Model Theory of Ordered Logics: Expressivity and Interpolation (Extended version)

Bednarczyk¹,

Jaakkola²

2022

Preprint

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“…Nevertheless, there are also more benign DL constructs regarding the complexity of CQ entailment. Examples are counting (Q) (Lutz 2008) (the complexity stays the same even for expressive arithmetical constraints (Baader, Bednarczyk, and Rudolph 2020)), role-hierarchies alone (H) (Eiter, Ortiz, and Simkus 2012) or even a tamed use of higher-arity relations (Bednarczyk 2021a).…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, this establishes 2EXPTIME-hardness of query entailment for the Z family (a.k.a. ALCHb Self reg ) of DLs (Calvanese, Eiter, and Ortiz 2009), which until now remained open as well as the 2EXPTIME-hardness of querying the forward guarded fragment (Bednarczyk 2021a) with equality.…”

Section: Introductionmentioning

confidence: 99%

The Price of Selfishness: Conjunctive Query Entailment for ALCSelf Is 2EXPTIME-Hard

Bednarczyk

Rudolph

2022

AAAI

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In logic-based knowledge representation, query answering has essentially replaced mere satisfiability checking as the inferencing problem of primary interest. For knowledge bases in the basic description logic ALC, the computational complexity of conjunctive query (CQ) answering is well known to be EXPTIME-complete and hence not harder than satisfiability. This does not change when the logic is extended by certain features (such as counting or role hierarchies), whereas adding others (inverses, nominals or transitivity together with role-hierarchies) turns CQ answering exponentially harder. We contribute to this line of results by showing the surprising fact that even extending ALC by just the Self operator – which proved innocuous in many other contexts – increases the complexity of CQ entailment to 2EXPTIME. As common for this type of problem, our proof establishes a reduction from alternating Turing machines running in exponential space, but several novel ideas and encoding tricks are required to make the approach work in that specific, restricted setting.

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“…21]), role-hierarchies alone (H) [EOS12,Cor. 3] or even a tamed use of higher-arity relations [Bed21,Thm. 20].…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, this establishes 2ExpTime-hardness of query entailment for the Z family (a.k.a. ALCHb Self reg ) of DLs [CEO09], which until now remained open 1 as well as the 2ExpTimehardness of querying ontologies formulated in the forward guarded fragment [Bed21] with equality. 2 Our proof goes via encoding of computational trees of alternating Turing machines working in exponential space and follows a general hardness-proof-scheme by Lutz [Lut08,Section 4].…”

Section: Introductionmentioning

confidence: 99%

The Price of Selfishness: Conjunctive Query Entailment for ALCSelf is 2ExpTime-hard

Bednarczyk¹,

Rudolph²

2021

Preprint

Self Cite

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In logic-based knowledge representation, query answering has essentially replaced mere satisfiability checking as the inferencing problem of primary interest. For knowledge bases in the basic description logic ALC, the computational complexity of conjunctive query (CQ) answering is well known to be ExpTimecomplete and hence not harder than satisfiability. This does not change when the logic is extended by certain features (such as counting or role hierarchies), whereas adding others (inverses, nominals or transitivity together with role-hierarchies) turns CQ answering exponentially harder.We contribute to this line of results by showing the surprising fact that even extending ALC by just the Self operator -which proved innocuous in many other contexts -increases the complexity of CQ entailment to 2ExpTime. As common for this type of problem, our proof establishes a reduction from alternating Turing machines running in exponential space, but several novel ideas and encoding tricks are required to make the approach work in that specific, restricted setting.

show abstract

Exploiting Forwardness: Satisfiability and Query-Entailment in Forward Guarded Fragment

Cited by 7 publications

References 15 publications

Towards a Model Theory of Ordered Logics: Expressivity and Interpolation (Extended version)

Towards a Model Theory of Ordered Logics: Expressivity and Interpolation (Extended version)

The Price of Selfishness: Conjunctive Query Entailment for ALCSelf Is 2EXPTIME-Hard

The Price of Selfishness: Conjunctive Query Entailment for ALCSelf is 2ExpTime-hard

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