. We explore a connection between different ways of representing information in computer science. We show that relational databases, modules, algebraic specifications and constraint systems all satisfy the same ten axioms. A commutative semigroup together with a lattice satisfying these axioms is then called an “information algebra”. We show that any compact consequence operator satisfying the interpolation and the deduction property induces an information algebra. Conversely, each finitary information algebra can be obtained from a consequence operator in this way. Finally (...) we show that arbitrary (not necessarily finitary) information algebras can be represented as some kind of abstract relational database called a tuple system. (shrink)

We show the adequacy of axioms and proof rules for strict and lazy functional programs. Our basic logic comprises a huge part of what is common to the two styles of functional programming. The logic for call-by-value is obtained by adding the axiom that says that all variables are defined, whereas the logic for call-by-name is obtained by adding the axiom that postulates the existence of an undefined object for each type. To show the correctness of the axiomatization we do (...) not use denotational semantics and the adequacy of the evaluation of programs with respect to the semantics. Instead we use the standard term models based on call-by-value and call-by-name evaluation. We introduce a new method to prove on the syntactical level the monotonicity of the evaluation of functional programs with unbounded recursion. The direct method yields results concerning the proof-theoretic strength of the axiomatization. As a side result we obtain a syntactical proof of the context lemma for simply typed lambda terms with recursion. (shrink)

The standard theory of logic programming is not applicable to Prolog programs even not to pure code. Modifying the theory to take account of reality more is the motivation of this article. For this purpose we introduce the ℓ-completion and the inductive extension of a logic program. Both are first-order theories in a language with operators for success, failure and termination of goals. The ℓ-completion of a logic program is a sound and complete axiomatization of the Prolog depth-first search under (...) certain natural conditions; the inductive extension of the ℓ-completion is a suitable theory for proving termination and equivalence of pure Prolog programs with negation. (shrink)