33,530 research outputs found
On specifying database updates
AbstractWe address the problem of formalizing the evolution of a database under the effect of an arbitrary sequence of update transactions. We do so by appealing to a first-order representation language called the situation calculus, which is a standard approach in artificial intelligence to the formalization of planning problems. We formalize database transactions in exactly the same way as actions in the artificial intelligence planning domain. This leads to a database version of the frame problem in artificial intelligence. We provide a solution to the frame problem for a special, but substantial, class of update transactions. Using the axioms corresponding to this solution, we provide procedures for determining whether a given sequence of update transactions is legal, and for query evaluation in an updated database. These procedures have the desirable property that they appeal to theorem-proving only with respect to the initial database state.We next address the problem of proving properties true in all states of the database. It turns out that mathematical induction is required for this task, and we formulate a number of suitable induction principles. Among those properties of database states that we wish to prove are the standard database notions of static and dynamic integrity constraints. In our setting, these emerge as inductive entailments of the database.Finally, we discuss various possible extensions of the approach of this paper, including transaction logs and historical queries, the complexity of query evaluation, actualized transactions, logic programming approaches to updates, database views, and state constraints
On specifying database updates
We address the problem of formalizing the evolution of a database under the effect of an
arbitrary sequence of update transactions. We do so by appealing to a first order representation
language called the situation calculus, which is a standard approach in artificial intelligence to
the formalization of planning problems. We formalize database transactions in exactly the same
way as actions in the artificial intelligence planning domain. This leads to a database version
of the frame problem in artificial intelligence. We provide a solution to the frame problem
for a special, but substantial, class of update transactions. Using the axioms corresponding
to this solution, we provide procedures for determining whether a given sequence of update
transactions is legal, and for query evaluation in an updated database. These procedures have
the nice property that they appeal to theorem-proving only with respect to the initial database state.
We next address the problem of proving properties true in ali states of the database. It
turns out that mathematical induction is required for this task, and we formulate a number of
suitable induction principies. Among those properties of database states that we wish to prove
are the standard database -notions of static and dynamic integrity constraints. In our setting,
these emerge as inductive entailments of the database.
Finally, we discuss various possible extensions of the approach of this paper, including transaction
logs and historical queries, the complexity of query evaluation, actualized transactions,
logic programming approaches to updates, database views and state constraints
Validating specifications of dynamic systems using automated reasoning techniques
In this paper, we propose a new approach to validating formal specifications of observable behavior of discrete dynamic systems. By observable behavior we mean system behavior as observed by users or other systems in the environment of the system. Validation of a formal specification of an informal domain tries to answer the question whether the specification actually describes the intended domain. This differs from the verification problem, which deals with the correspondence between formal objects, e.g. between a formal specification of a system and an implementation of it. We consider formal specifications of object-oriented dynamic systems that are subject to static and dynamic integrity constraints. To validate that such a specification expresses the intended behavior, we propose to use a tool that can answer reachability queries. In a reachability query we ask whether the system can evolve from one state into another without violating the integrity constraints. If the query is answered positively, the system should exhibit an example path between the states; if the answer is negative, the system should explain why this is so. An example path produced by the tool can be used to produce scenarios for presentations of system behavior, but can also be used as a basis for acceptance testing. In this paper, we discuss the use of planning and theoremproving techniques to answer such queries, and illustrate the use of reachability queries in the context of information system development
Bounded Situation Calculus Action Theories
In this paper, we investigate bounded action theories in the situation
calculus. A bounded action theory is one which entails that, in every
situation, the number of object tuples in the extension of fluents is bounded
by a given constant, although such extensions are in general different across
the infinitely many situations. We argue that such theories are common in
applications, either because facts do not persist indefinitely or because the
agent eventually forgets some facts, as new ones are learnt. We discuss various
classes of bounded action theories. Then we show that verification of a
powerful first-order variant of the mu-calculus is decidable for such theories.
Notably, this variant supports a controlled form of quantification across
situations. We also show that through verification, we can actually check
whether an arbitrary action theory maintains boundedness.Comment: 51 page
An Introduction to Mechanized Reasoning
Mechanized reasoning uses computers to verify proofs and to help discover new
theorems. Computer scientists have applied mechanized reasoning to economic
problems but -- to date -- this work has not yet been properly presented in
economics journals. We introduce mechanized reasoning to economists in three
ways. First, we introduce mechanized reasoning in general, describing both the
techniques and their successful applications. Second, we explain how mechanized
reasoning has been applied to economic problems, concentrating on the two
domains that have attracted the most attention: social choice theory and
auction theory. Finally, we present a detailed example of mechanized reasoning
in practice by means of a proof of Vickrey's familiar theorem on second-price
auctions
Towards an Intelligent Tutor for Mathematical Proofs
Computer-supported learning is an increasingly important form of study since
it allows for independent learning and individualized instruction. In this
paper, we discuss a novel approach to developing an intelligent tutoring system
for teaching textbook-style mathematical proofs. We characterize the
particularities of the domain and discuss common ITS design models. Our
approach is motivated by phenomena found in a corpus of tutorial dialogs that
were collected in a Wizard-of-Oz experiment. We show how an intelligent tutor
for textbook-style mathematical proofs can be built on top of an adapted
assertion-level proof assistant by reusing representations and proof search
strategies originally developed for automated and interactive theorem proving.
The resulting prototype was successfully evaluated on a corpus of tutorial
dialogs and yields good results.Comment: In Proceedings THedu'11, arXiv:1202.453
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