An Approach to Representing the Process of Information Business Modeling

The compact and visualized documenting of information business modeling is a major prerequisite for comprehending its basic concepts, as well as for its effective application and improvement. The documenting of this process is related to its modeling. Thus, the process of information business modeling can be represented by its own tools. Being based on this thesis, the authors suggest an approach to representing the process of information business modeling. A profile for its documenting has been developed for the purpose.

Representing of the Bulgarian Institutions: National Archives

Digitisation as an opportunity for Bulgarian National Archives to fulfill its functions as a heritage Institution and a government agency according to the new standards.

Representing "Recursive" Default Logic in Modal Logic

The "recursive" definition of Default Logic is shown to be representable in a monotonic Modal Quantificational Logic whose modal laws are stronger than S5. Specifically, it is proven that a set of sentences of First Order Logic is a fixed-point of the "recursive" fixed-point equation of Default Logic with an initial set of axioms and defaults if and only if the meaning of the fixed-point is logically equivalent to a particular modal functor of the meanings of that initial set of sentences and of the sentences in those defaults. This is important because the modal representation allows the use of powerful automatic deduction systems for Modal Logic and because unlike the original "recursive" definition of Default Logic, it is easily generalized to the case where quantified variables may be shared across the scope of the components of the defaults.

On OBDD Transformations Representing Finite State Automata

We present OBDD transformation problem representing finite labeled transition systems corresponding to some congruence relation. Transformations are oriented toward obtaining the OBDD of a minimized transition system for this congruence relation.

Representing Reflective Logic in Modal Logic

The nonmonotonic logic called Reflective Logic is shown to be representable in a monotonic Modal Quantificational Logic whose modal laws are stronger than S5. Specifically, it is proven that a set of sentences of First Order Logic is a fixed-point of the fixed-point equation of Reflective Logic with an initial set of axioms and defaults if and only if the meaning of that set of sentences is logically equivalent to a particular modal functor of the meanings of that initial set of sentences and of the sentences in those defaults. This result is important because the modal representation allows the use of powerful automatic deduction systems for Modal Logic and because unlike the original Reflective Logic, it is easily generalized to the case where quantified variables may be shared across the scope of the components of the defaults thus allowing such defaults to produce quantified consequences. Furthermore, this generalization properly treats such quantifiers since all the laws of First Order Logic hold and since both the Barcan Formula and its converse hold.

Representing Default Logic in Modal Logic

The nonmonotonic logic called Default Logic is shown to be representable in a monotonic Modal Quantificational Logic whose modal laws are stronger than S5. Specifically, it is proven that a set of sentences of First Order Logic is a fixed-point of the fixed-point equation of Default Logic with an initial set of axioms and defaults if and only if the meaning or rather disquotation of that set of sentences is logically equivalent to a particular modal functor of the meanings of that initial set of sentences and of the sentences in those defaults. This result is important because the modal representation allows the use of powerful automatic deduction systems for Modal Logic and because unlike the original Default Logic, it is easily generalized to the case where quantified variables may be shared across the scope of the components of the defaults thus allowing such defaults to produce quantified consequences. Furthermore, this generalization properly treats such quantifiers since both the Barcan Formula and its converse hold.

Representing Autoepistemic Logic in Modal Logic

The nonmonotonic logic called Autoepistemic Logic is shown to be representable in a monotonic Modal Quantificational Logic whose modal laws are stronger than S5. Specifically, it is proven that a set of sentences of First Order Logic is a fixed-point of the fixed-point equation of Autoepistemic Logic with an initial set of axioms if and only if the meaning or rather disquotation of that set of sentences is logically equivalent to a particular modal functor of the meaning of that initial set of sentences. This result is important because the modal representation allows the use of powerful automatic deduction systems for Modal Logic and unlike the original Autoepistemic Logic, it is easily generalized to the case where quantified variables may be shared across the scope of modal expressions thus allowing the derivation of quantified consequences. Furthermore, this generalization properly treats such quantifiers since both the Barcan formula and its converse hold.

Representing Equivalence Problems for Combinatorial Objects

Methods for representing equivalence problems of various combinatorial objects as graphs or binary matrices are considered. Such representations can be used for isomorphism testing in classification or generation algorithms. Often it is easier to consider a graph or a binary matrix isomorphism problem than to implement heavy algorithms depending especially on particular combinatorial objects. Moreover, there already exist well tested algorithms for the graph isomorphism problem (nauty) and the binary matrix isomorphism problem as well (Q-Extension). ACM Computing Classification System (1998): F.2.1, G.4.