An auxiliary logic on trees: On the tower-hardness of logics featuring reachability and submodel reasoning

Mansutti, Alessio

doi:10.1016/j.ic.2022.104911

Cited by 1 publication

(2 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This work can be continued in several directions. For instance, Tower-hardness of SAT(QCTL t F ) is recently refined in [Man20b,Man20a] by establishing that already QCTL t F restricted to formulae of modal/temporal depth two is also Tower-hard. Among the several directions, one of them would be to characterise the expressiveness of QCTL t X or QCTL t F along the lines of [DLM16] or [Kuu15], see also [AvBG18].…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Why Does Propositional Quantification Make Modal and Temporal Logics on Trees Robustly Hard?

Bednarczyk¹,

Demri²

2022

Logical Methods in Computer Science

View full text Add to dashboard Cite

Adding propositional quantification to the modal logics K, T or S4 is known to lead to undecidability but CTL with propositional quantification under the tree semantics (tQCTL) admits a non-elementary Tower-complete satisfiability problem. We investigate the complexity of strict fragments of tQCTL as well as of the modal logic K with propositional quantification under the tree semantics. More specifically, we show that tQCTL restricted to the temporal operator EX is already Tower-hard, which is unexpected as EX can only enforce local properties. When tQCTL restricted to EX is interpreted on N-bounded trees for some N >= 2, we prove that the satisfiability problem is AExpPol-complete; AExpPol-hardness is established by reduction from a recently introduced tiling problem, instrumental for studying the model-checking problem for interval temporal logics. As consequences of our proof method, we prove Tower-hardness of tQCTL restricted to EF or to EXEF and of the well-known modal logics such as K, KD, GL, K4 and S4 with propositional quantification under a semantics based on classes of trees.

show abstract

Section: Discussionmentioning

confidence: 99%

“…In order to show that SAT(QCTL t F ) is Tower-hard, we design a logarithmic-space many-one reduction from SAT(QCTL t X ). A more sophisticated analysis is also possible to establish Tower-hardness for even smaller fragments, see the recent work [Man20a].…”

Section: A Harvest Of Tower-complete Modal and Temporal Logicsmentioning

confidence: 99%

Why Does Propositional Quantification Make Modal and Temporal Logics on Trees Robustly Hard?

Bednarczyk¹,

Demri²

2022

Logical Methods in Computer Science

View full text Add to dashboard Cite

show abstract

An auxiliary logic on trees: On the tower-hardness of logics featuring reachability and submodel reasoning

Cited by 1 publication

References 33 publications

Why Does Propositional Quantification Make Modal and Temporal Logics on Trees Robustly Hard?

Why Does Propositional Quantification Make Modal and Temporal Logics on Trees Robustly Hard?

Contact Info

Product

Resources

About