An early version of the Z Standard included the deductive system W for reasoning about Z specifications. Later versions contain a different deductive system. In this paper we sketch a proof that W is relatively sound with respect to this new deductive system. We do this by demonstrating a semantic basis for a correspondence between the two systems, then showing that each of the inference rules ...

This paper presents a method for integrating deductive databases. In our approach deductive databases are expressed in a functional database programming language in which rules are expressed as derived functions. For integrating the extensional parts of deductive databases, we use a binary relational ER model with subtyping as the common data model and propose a semi-automatic method to perform...

Motivated by the possibilities of applying deductive database technology for efficient query answering in description logics, we present a translation operator μ that transforms non-recursive ALC ontologies into a disjunctive deductive database. Contrary to our previous work, in this paper we focus on handling negation, disjunction and existential quantifiers, which cannot be handled by deducti...

Standard logic is a package with two parts – a formal deductive apparatus and a conception of interpretation for the language. The deductive apparatus and the semantics are mutually reinforcing and in this chapter we examine primarily the semantic assumptions that formally justify the deductive machinery. The second part of the package, the semantics of ‘standard’ logic, includes the assumption...

Induction and abduction are well known non-deductive inferences. We shall propose that design is also another form of non-deductive inference, and, based on Barwise and Seligman’s mathematical theory of information flow, construct a formal model of non-deductive inferences. We shall show also that these inferences are interpretable each other, and argue mathematical properties of the model.

We propose an original approach for checking memory safety of C pointer programs, by combining deductive verification and abstract interpretation techniques. The approach is modular and contextual, thanks to the use of Hoare-style annotations (preand postconditions), allowing us to verify each C function independently. Deductive verification is used to check these annotations in a sound way. Ab...

Deductive reasoning is the kind of reasoning in which, roughly, the truth of the input propositions (the premises) logically guarantees the truth of the output proposition (the conclusion), provided that no mistake has been made in the reasoning. The premises may be propositions that the reasoner believes or assumptions that the reasoner is exploring. Deductive reasoning contrasts with inductiv...

The framework of algorithmic knowledge assumes that agents use algorithms to compute the facts they explicitly know. In many cases of interest, a deductive system, rather than a particular algorithm, captures the formal reasoning used by the agents to compute what they explicitly know. We introduce a logic for reasoning about both implicit and explicit knowledge with the latter defined with res...

LEWIS (1988) made the case that today’s biology is essentially hypothetico-deductive in nature. In Lewis’s view, biology is not a science in which one gathers all the facts, classifies them and then somehow crystallizes them into theory. In Lewis’s words, ‘‘This erroneous view of method plus the absence of a proper definition of theory misguided my early development in science’’ (p. 362). The f...