Temporal attribute implications

Mgr. Jan TŘÍSKA

Doctoral thesis

Temporal data dependencies

Abstract:

We deal with dependencies in object-attribute data which is recorded at separate points in time. The data is formalized by finitely many tables encoding the relationship between the objects and the attributes and each table can be seen as a single formal context observed at a separate point in time. Given such data, we are interested in concise ways of characterizing all if-then dependencies between the attributes that hold in the data and are preserved in all time points. In order to formalize the dependencies, we introduce if-then formulas called temporal attribute implications which can be seen as particular formulas of linear temporal logic. We introduce a semantic entailment of the formulas, show its fixed-point characterization, investigate closure properties of model classes, present an axiomatization and prove its completeness, and investigate alternative axiomatizations and normalized proofs. We investigate decidability and complexity issues of the logic and prove that the entailment problem is NP-hard and belongs to EXPSPACE. We show that by restricting to predictive formulas, the entailment problem is decidable in pseudo-linear time. We introduce non-redundant bases of dependencies from data as non-redundant sets entailing exactly all the dependencies that hold in the data. In addition, we investigate minimality of bases as a stronger form of non-redundancy. For given data, we present a description of minimal bases using the notion of pseudo-intents generalized in the temporal setting. We further investigate properties of minimal sets of formulas and present sufficient and necessary conditions for their characterization.In addition to the characterization of minimality, we present an algorithm that can be used to minimize any finite set of temporal attribute implications.

Abstract:

We deal with dependencies in object-attribute data which is recorded at separate points in time. The data is formalized by finitely many tables encoding the relationship between the objects and the attributes and each table can be seen as a single formal context observed at a separate point in time. Given such data, we are interested in concise ways of characterizing all if-then dependencies between the attributes that hold in the data and are preserved in all time points. In order to formalize the dependencies, we introduce if-then formulas called temporal attribute implications which can be seen as particular formulas of linear temporal logic. We introduce a semantic entailment of the formulas, show its fixed-point characterization, investigate closure properties of model classes, present an axiomatization and prove its completeness, and investigate alternative axiomatizations and normalized proofs. We investigate decidability and complexity issues of the logic and prove that the entailment problem is NP-hard and belongs to EXPSPACE. We show that by restricting to predictive formulas, the entailment problem is decidable in pseudo-linear time. We introduce non-redundant bases of dependencies from data as non-redundant sets entailing exactly all the dependencies that hold in the data. In addition, we investigate minimality of bases as a stronger form of non-redundancy. For given data, we present a description of minimal bases using the notion of pseudo-intents generalized in the temporal setting. We further investigate properties of minimal sets of formulas and present sufficient and necessary conditions for their characterization.In addition to the characterization of minimality, we present an algorithm that can be used to minimize any finite set of temporal attribute implications.

Keywords

attribute implication, axiomatization, minimality, non-redundancy, temporal data, temporal semantics

Language used: English

Date on which the thesis was submitted / produced: 7. 6. 2018

Thesis defence

• Supervisor: doc. RNDr. Vilém Vychodil, Ph.D.

PALACKÝ UNIVERSITY OLOMOUC

Faculty of Science

Doctoral programme / field:
Computer Science / Computer Science