Determining Structural Descriptions by Boolean Formulas
نویسندگان
چکیده
A new numerical approach of nding out the full and reduced structural descriptions of an object (image) or class is suggested in the paper. These structural descriptions are based on the Boolean formulas obtained by a learning procedure. The conjunctions for each object at the rst level of generalization are considered as features. At the next level of generalization the relationship between conjunctions and classes are introduced. For determining the reduced structural descriptions for objects and classes some optimization procedures are also proposed. A numerical example illustrating the suggested approach is given.
منابع مشابه
A structural approach to reasoning with quantified Boolean formulas
In this paper we approach the problem of reasoning with quantified Boolean formulas (QBFs) by combining search and resolution, and by switching between them according to structural properties of QBFs. We provide empirical evidence that QBFs which cannot be solved by search or resolution alone, can be solved by combining them, and that our approach makes a proof-of-concept implementation competi...
متن کاملDichotomy Theorems for Alternation-Bounded Quantified Boolean Formulas
In 1978, Schaefer proved his famous dichotomy theorem for generalized satisfiability problems. He defined an infinite number of propositional satisfiability problems, showed that all these problems are either in P or NP-complete, and gave a simple criterion to determine which of the two cases holds. This result is surprising in light of Ladner’s theorem, which implies that there are an infinite...
متن کاملVersion Spaces, Structural Descriptions and NP-Completeness
This paper provides a logical analysis of the problem of version space maintenance which highlights fundamental differences between version spaces of boolean concepts and version spaces for structural descriptions. It then employs the theory of NP-completeness in a heuristic manner to isolate a variety of respects in which the standard version space maintenance procedure is intractable in the c...
متن کاملOn the Complexities of Selected Satisfiability and Equivalence Queries over Boolean Formulas and Inclusion Queries over Hulls
This paper is concerned with the computational complexities of three types of queries, namely, satisfiability, equivalence, and hull inclusion. The first two queries are analyzed over the domain of CNF formulas, while hull inclusion queries are analyzed over continuous and discrete sets defined by rational polyhedra. Although CNF formulas can be represented by polyhedra over discrete sets, we a...
متن کاملRepresenting Policies for Quantified Boolean Formulas
The practical use of Quantified Boolean Formulas (QBFs) often calls for more than solving the validity problem QBF. For this reason we investigate the corresponding function problems whose expected outputs are policies. QBFs which do not evaluate to true do not have any solution policy, but can be of interest nevertheless; for handling them, we introduce a notion of partial policy. We focus on ...
متن کامل