We propose a language which can express every computable query. The language is syntactically based on the first-order predicate calculus, but semantically is interpreted as post-conditions, unlike the customary calculus query languages. The language has a capability to restrict itself to reasonable queries, accepting criteria of reasonability as a parameter.

Let / be any fixed positive integer and a a sentence in the first-order predicate calculus of/unary functions. For positive integers n, an «-structure is a model with universe {0,1,...,« 1} and/unary functions, and p(n,a) is the ratio of the number of «-structures satisfying a to n"f, the number of «-structures. We show that lim„_00/i(«, a) exists for all such a, and its value is given by an ex...

We investigate a construction schema for first-order logical systems, called “form logic”. Form logic allows us to overcome the dualistic commitment of predicate logic to individual constants and predicates. Dualism is replaced by a pluralism of terms of different “logical forms”. Individual form-logical systems are generated by the determination of a range of logical forms and of the formbased...

a new method was developed for the spectral resolution by further determination of three- and  four-component  mixtures  of  drugs in urine samples through  the complementary application of multivariate curve resolution-alternating least squares with correlation  constraint. in the current study, a simple method was proposed to construct a calibration set for the mixture of drugs in the presenc...

Rough set theory is an effective tool for data mining. According to the theory, a concept is definable if it can be written as a Boolean combination of equivalence classes induced from classification attributes. On the other hand, definability in logic has been explicated by Beth’s theorem. In this paper, we propose two data representation formalisms, called first-order data logic (FODL) and at...

We present a two-layer language for the specification of database evolution in terms of transaction-based, dynamic integrity constraints. The first language layer is based on first-order logic and it is used to express dynamic constraints in terms of queries on the transaction history of a database. The second layer uses a customizable combination of text and graphics and its semantics are defi...

Students find logic hard. In particular, they seem to find it hard to translate natural language sentences into their corresponding representations in logic. As an enabling step towards determining why this is the case, this paper presents the public release of a corpus of over 4.5 million translations of natural language (nl) sentences into first-order logic (fol), provided by 55,000 students ...

A classical problem in database theory is to verify whether there exists a relation (or database) instance satisfying a number of given dependency constraints but the issue of handling constraints on aggregate data has not been much investigated so far. This paper introduces a new type of data dependency, called count constraint, that requires the results of given count operations on a relation...