Abductive hypotheses generation in neural-symbolic systems

Wydział Nauk SpołecznychCelem pracy było opracowanie procedury abdukcyjnej, która działa w oparciu o system neuronalno-symboliczny. Procedura abdukcyjna jest rozumiana jako rozszerzona interpretacja algorytmiczna rozumowania abdukcyjnego, tj. posiadając wiedzę Γ oraz zjawisko ᵠ, którego nie można wyprowadzić z Γ tworzymy nową bazę wiedzy Γ’, która jest zmodyfikowaną wersją Γ, a z której ᵠ jest osiągalne. Hipotezę abdukcyjną definiujemy jako różnicę symetryczną pomiędzy Γ i Γ’. Wymagamy aby powstałe w ten sposób hipotezy abdukcyjne posiadały pewne własności, np. niesprzeczność z bazą wiedzy. Procedura abdukcyjna zaimplementowana została w systemie neuronalno-symbolicznym, który umożliwia tłumaczenie programów logicznych (baza wiedzy Γ oraz cel abdukcyjny ᵠ) na sztuczne sieci neuronowe, uczenie sieci neuronowych przy pomocy algorytmu propagacji wstecznej (proces tworzenia hipotezy abdukcyjnej) oraz tłumaczenie sieci neuronowych na programy logiczne (baza wiedzy Γ’), co umożliwia otrzymanie hipotezy abdukcyjnej.The goal of this work was to create abductive procedure that is implemented in neural-symbolic system. The abductive procedure is understood as extended algorithmic perspective, i.e. having Γ as knowledge base and ᵠ that is not obtainable from Γ we create Γ’ (modified Γ) from which ᵠ is obtainable. The abductive hypothesis is a symmetric difference between Γ and Γ’. We also require abductive hypotheses to fulfill certain conditions. The procedure is implemented in a neural-symbolic system where Γ and ᵠ are represented as a logic program that is translated into a neural network, the neural network is then trained by means of the backpropagation algorithm in such a way that ᵠ becomes obtainable, and then the trained neural network is translated back into a logic program that represents Γ’. The symmetric difference between Γ and Γ’ is the abductive hypothesis

Integrity constraints in deductive databases

A deductive database is a logic program that generalises the concept of a relational database. Integrity constraints are properties that the data of a database are required to satisfy and in the context of logic programming, they are expressed as closed formulae. It is desirable to check the integrity of a database at the end of each transaction which changes the database. The simplest approach to checking integrity in a database involves the evaluation of each constraint whenever the database is updated. However, such an approach is too inefficient, especially for large databases, and does not make use of the fact that the database satisfies the constraints prior to the update. A method, called the path finding method, is proposed for checking integrity in definite deductive databases by considering constraints as closed first order formulae. A comparative evaluation is made among previously described methods and the proposed one. Closed general formulae is used to express aggregate constraints and Lloyd et al. 's simplification method is generalised to cope with these constraints. A new definition of constraint satisfiability is introduced in the case of indefinite deductive databases and the path finding method is generalised to check integrity in the presence of static constraints only. To evaluate a constraint in an indefinite deductive database to take full advantage of the query evaluation mechanism underlying the database, a query evaluator is proposed which is based on a definition of semantics, called negation as possible failure, for inferring negative information from an indefinite deductive database. Transitional constraints are expressed using action relations and it is shown that transitional constraints can be handled in definite deductive databases in the same way as static constraints if the underlying database is suitably extended. The concept of irnplicit update is introduced and the path finding method is extended to compute facts which are present in action relations. The extended method is capable of checking integrity in definite deductive databases in the presence of transitional constraints. Combining different generalisations of the path finding method to check integrity in deductive databases in the presence of arbitrary constraints is discussed. An extension of the data manipulation language of SQL is proposed to express a wider range of integrity constraints. This class of constraints can be maintained in a database with the tools provided in this thesis