90,037 research outputs found
A TEMPORAL RELATIONAL ALGEBRA AS A BASIS FOR TEMPORAL RELATIONAL COMPLETENESS
We define a temporal algebra that is applicable to any
temporal relational data model supporting discrete linear
bounded time. This algebra has the five basic
relational algebra operators extended to the temporal
domain and an operator of linear recursion. We
show that this algebra has the expressive power of a
safe temporal calculus based on the predicate temporal
logic with the until and since temporal operators.
In [CrC189], a historical calculus was proposed as a
basis for historical relational completeness. We propose
the temporal algebra defined in this paper and
the equivalent temporal calculus as an alternative basis
for temporal relational completeness.Information Systems Working Papers Serie
ON COMPLETENESS OF HISTORICAL RELATIONAL QUERY LANGUAGES
Numerous proposals for extending the relational data model to incorporate the temporal
dimension of data have appeared in the past several years. These proposals have differed
considerably in the way that the temporal dimension has been incorporated both into the
structure of the extended relations of these temporal models, and consequently into the
extended relational algebra or calculus that they define. Because of these differences it has
been difficult to compare the proposed models and to make judgments as to which of them
might in some sense be equivalent or even better. In this paper we define the notions of
temporally grouped and temporally ungrouped historical data models and propose
two notions of historical relational completeness, analogous to Codd's notion of relational
completeness, one for each type of model. We show that the temporally ungrouped
models are less powerful than the grouped models, but demonstrate a technique for extending
the ungrouped models with a grouping mechanism to capture the additional semantic
power of temporal grouping. For the ungrouped models we define three different languages,
a temporal logic, a logic with explicit reference to time, and a temporal algebra, and show
that under certain assumptions all three are equivalent in power. For the grouped models
we define a many-sorted logic with variables over ordinary values, historical values, and
times. Finally, we demonstrate the equivalence of this grouped calculus and the ungrouped
calculus extended with the proposed grouping mechanism. We believe the classification of
historical data models into grouped and ungrouped provides a useful framework for the
comparison of models in the literature, and furthermore the exposition of equivalent languages
for each type provides reasonable standards for common, and minimal, notions of
historical relational completeness.Information Systems Working Papers Serie
G\"odel-Dummett linear temporal logic
We investigate a version of linear temporal logic whose propositional
fragment is G\"odel-Dummett logic (which is well known both as a
superintuitionistic logic and a t-norm fuzzy logic). We define the logic using
two natural semantics: first a real-valued semantics, where statements have a
degree of truth in the real unit interval and second a `bi-relational'
semantics. We then show that these two semantics indeed define one and the same
logic: the statements that are valid for the real-valued semantics are the same
as those that are valid for the bi-relational semantics. This G\"odel temporal
logic does not have any form of the finite model property for these two
semantics: there are non-valid statements that can only be falsified on an
infinite model. However, by using the technical notion of a quasimodel, we show
that every falsifiable statement is falsifiable on a finite quasimodel,
yielding an algorithm for deciding if a statement is valid or not. Later, we
strengthen this decidability result by giving an algorithm that uses only a
polynomial amount of memory, proving that G\"odel temporal logic is
PSPACE-complete. We also provide a deductive calculus for G\"odel temporal
logic, and show this calculus to be sound and complete for the above-mentioned
semantics, so that all (and only) the valid statements can be proved with this
calculus.Comment: arXiv admin note: substantial text overlap with arXiv:2205.00574,
arXiv:2205.0518
On Completeness of Historical Relational Query Languages
Numerous proposals for extending the relational data model to incorporate the temporal
dimension of data have appeared in the past several years. These proposals have differed
considerably in the way that the temporal dimension has been incorporated both into the
structure of the extended relations of these temporal models, and consequently into the
extended relational algebra or calculus that they define. Because of these differences it
has been difficult to compare the proposed models and to make judgments as to which of
them might in some sense be equivalent or even better. In this paper we define the notions of
temporally grouped and temporally ungrouped historical data models and propose two
notions of historical reIationa1 completeness, analogous to Codd's notion of relational
completeness, one for each type of model. We show that the temporally ungrouped models
are less expressive than the grouped models, but demonstrate a technique for extending the
ungrouped models with a grouping mechanism to capture the additional semantic power
of temporal grouping. For the ungrouped models we define three different languages, a
temporal logic, a logic with explicit reference to time, and a temporal algebra, and show
that under certain assumptions all three are equivalent in power. For the grouped models
we define a many-sorted logic with variables over ordinary values, historical values, and
times. Finally, we demonstrate the equivalence of this grouped calculus and the ungrouped
calculus extended with a grouping mechanism. We believe the classification of historical
data models into grouped and ungrouped provides a useful framework for the comparison
of models in the literature, and furthermore the exposition of equivalent languages for each
type provides reasonable standards for common, and minimal, notions of historical relational
completeness.Information Systems Working Papers Serie
FORMAL SEMANTICS FOR TIME IN DATABASES
The concept of an historical database is introduced as a tool for
modelling the dynamic nature of some part of the real world. Just as first-order
logic has been shown to be a useful formalism for expressing and
understanding the underlying semantics of the relational database model,
intensional logic is presented as an analogous formalism for expressing and
understanding the temporal semantics involved in an historical database.
The various components of the relational model, as extended to include
historical relations, are discussed in terms of the model theory for the logic
ILs, a variation of the logic IL formulated by Richard Montague. The
modal concepts of intensional and extensional data constraints and
queries are introduced and contrasted. Finally, the potential application of
these ideas to the problem of Natural Language Database Querying is discussed.Information Systems Working Papers Serie
Refinement Calculus of Reactive Systems
Refinement calculus is a powerful and expressive tool for reasoning about
sequential programs in a compositional manner. In this paper we present an
extension of refinement calculus for reactive systems. Refinement calculus is
based on monotonic predicate transformers, which transform sets of post-states
into sets of pre-states. To model reactive systems, we introduce monotonic
property transformers, which transform sets of output traces into sets of input
traces. We show how to model in this semantics refinement, sequential
composition, demonic choice, and other semantic operations on reactive systems.
We use primarily higher order logic to express our results, but we also show
how property transformers can be defined using other formalisms more amenable
to automation, such as linear temporal logic (suitable for specifications) and
symbolic transition systems (suitable for implementations). Finally, we show
how this framework generalizes previous work on relational interfaces so as to
be able to express systems with infinite behaviors and liveness properties
From BDI and stit to bdi-stit logic
Since it is desirable to be able to talk about rational agents forming attitudes toward their concrete agency, we suggest an introduction of doxastic, volitional, and intentional modalities into the multi-agent logic of deliberatively seeing to it that, dstit logic. These modalities are borrowed from the well-known BDI (belief-desire-intention) logic. We change the semantics of the belief and desire operators from a relational one to a monotonic neighbourhood semantic in order to handle ascriptions of conflicting but not inconsistent beliefs and desires as being satisfiable. The proposed bdi-stit logic is defined with respect to branching time frames, and it is shown that this logic is a generalization of a bdi logic based on branching time possible worlds frames (but without temporal operators) and dstit logic. The new bdi-stit logic generalizes bdi and dstit logic in the sense that for any model of bdi or dstit logic, there is an equivalent bdi-stit model
ON COMPLETENESS OF HISTORICAL RELATIONAL QUERY LANGUAGES
Numerous proposals for extending the relational data model to incorporate the temporal
dimension of data have appeared in the past several years. These proposals have differed
considerably in the way that the temporal dimension has been incorporated both into the
structure of the extended relations of these temporal models, and consequently into the
extended relational algebra or calculus that they define. Because of these differences it has
been difficult to compare the proposed models and to make judgments as to which of them
might in some sense be equivalent or even better. In this paper we define the notions of
temporally grouped and temporally ungrouped historical data models and propose
two notions of historical relational completeness, analogous to Codd's notion of relational
completeness, one for each type of model. We show that the temporally ungrouped
models are less powerful than the grouped models, but demonstrate a technique for extending
the ungrouped models with a grouping mechanism to capture the additional semantic
power of temporal grouping. For the ungrouped models we define three different languages,
a temporal logic, a logic with explicit reference to time, and a temporal algebra, and show
that under certain assumptions all three are equivalent in power. For the grouped models
we define a many-sorted logic with variables over ordinary values, historical values, and
times. Finally, we demonstrate the equivalence of this grouped calculus and the ungrouped
calculus extended with the proposed grouping mechanism. We believe the classification of
historical data models into grouped and ungrouped provides a useful framework for the
comparison of models in the literature, and furthermore the exposition of equivalent languages
for each type provides reasonable standards for common, and minimal, notions of
historical relational completeness.Information Systems Working Papers Serie
A Critical Review of Temporal Database Management Systems
There have been significant research activities in Temporal Databases during the last decade. However, the developments of a semantics of time, a temporal model for efficient database systems and temporal query languages still need much study. Based on the researches of the TDB group [Snodgrass 1987], the review of research about TDBMS in this dissertation mainly emphasises three aspects as follows. 1) The formulation of a semantics of time at the conceptual level. A topology of time and types of time attributes are introduced. A new taxonomy for time attributes is presented: assertion time, event time, and recording time. 2) The development of a model for TDBMS analogous to relational databases. Based on Snodgrass' classification, four kinds of databases: snapshot, rollback, historical and temporal are discussed in depth. But the discussion distinguishes some important differences from the representation of the TDB model: - historical relation for most enterprises is an interval relation, but not a sequence of snapshot slices indexed by valid time. The term "tuple" no longer simply refers to an entity as in traditional relational databases. It refers to different level representations of an object: entity, entity state, observation of entity, and observation of entity state in different types of databases. 3) The design of temporal query languages. We do not present a new temporal query language in this dissertation, but we discuss a Quel-like temporal query language, TQuel, in some depth. TQuel is compared with two other temporal query languages TOSQL and Legol 2.0. We centre the main discussion on TQuel's semantics for tuple calculus. The classification for the relationships between overlapping intervals suggests an approach using temporal logic to classify the derived tuples in tuple calculus. Under such an approach, a new presentation for tuple modification calculus is proposed, not only for interval relations, but also for event relations
Querying Schemas With Access Restrictions
We study verification of systems whose transitions consist of accesses to a
Web-based data-source. An access is a lookup on a relation within a relational
database, fixing values for a set of positions in the relation. For example, a
transition can represent access to a Web form, where the user is restricted to
filling in values for a particular set of fields. We look at verifying
properties of a schema describing the possible accesses of such a system. We
present a language where one can describe the properties of an access path, and
also specify additional restrictions on accesses that are enforced by the
schema. Our main property language, AccLTL, is based on a first-order extension
of linear-time temporal logic, interpreting access paths as sequences of
relational structures. We also present a lower-level automaton model,
Aautomata, which AccLTL specifications can compile into. We show that AccLTL
and A-automata can express static analysis problems related to "querying with
limited access patterns" that have been studied in the database literature in
the past, such as whether an access is relevant to answering a query, and
whether two queries are equivalent in the accessible data they can return. We
prove decidability and complexity results for several restrictions and variants
of AccLTL, and explain which properties of paths can be expressed in each
restriction.Comment: VLDB201
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