This article studies (multilayer perceptron) neural networks with an emphasis on the transformations involved — both forward and backward — in order to develop a semantical/logical perspective that is in line with standard program semantics. The common two-pass neural network training algorithms make this viewpoint particularly fitting. In the forward direction, neural networks act as state tra...

Kleene algebras with domain are Kleene algebras endowed with an operation that maps each element of the algebra to its domain of definition (or its complement) in abstract fashion. They form a simple algebraic basis for Hoare logics, dynamic logics or predicate transformer semantics. We formalise a modular hierarchy of algebras with domain and antidomain (domain complement) operations in Isabel...

The temporal property`to-always' has been proposed for specifying progress properties of concurrent programs. Although thèto-always' properties are a subset of thèleads-to' properties for a given program, `to-always' has more convenient proof rules and in some cases more accurately describes the desired system behavior. In this paper, we give a predicate transformer wta, derive some of its prop...

Simulation rules provide a simple, sound and complete technique for proving that one data type reenes another. This paper expresses the dependence of the sound-ness and completeness on the programming language by showing how sound and complete simulation rules for a given language are derived from those for its sublanguages. The dependence of the completeness on the semantic model is expressed ...

In this paper we revisit the well-known technique of predicate abstraction to characterise performance attributes of system models incorporating probability. We recast the theory using expectation transformers [8], and identify transformer properties which correspond to abstractions that yield nevertheless exact bound on the performance of infinite state probabilistic systems. In addition, we e...

Modal Kleene algebras are Kleene algebras with forward and backward modal operators, defined via domain and codomain operations. They provide a concise and convenient algebraic framework that subsumes various popular calculi and allows treating quite a number of areas. We survey the basic theory and some prominent applications. These include, on the system semantics side, wlp and wp calculus, P...

The behaviour of logic programs (with various built-in's) is described in terms of sets of substitutions associated with the control points of the program. These sets are deened by means of an operational semantics O, based on a description of uniication as predicate transformer. It is shown that O subsumes the semantics of logic programs consisting of the set of computed substitutions obtained...

We show that the set of valid formulas in Lukasiewicz predicate logic is a complete Π 2 set. We also show that the classically valid formulas are exactly those formulas in the classical language whose fuzzy value is 1/2. Lukasiewicz’ infinite valued logic can be seen as a particular “implementation” of fuzzy logic. The set of possible “truth values” (or, in another interpretation, degrees of ce...

Current body weight-based protein recommendations are ignoring the large variability in body composition, particularly lean mass (LM), which drives protein requirements. We explored and highlighted the inter-individual variability of weight versus body composition-adjusted protein intakes by secondary analysis in three cohorts of (1) 574 healthy adults (mean ± SD age: 41.4 ± 15.2 years); (2) 40...

The paper deals with fuzzy Horn logic (FHL) which is a fragment of predicate fuzzy logic with evaluated syntax. Formulas of FHL are of the form of simple implications between identities. We show that one can have Pavelka-style completeness of FHL w. r. t. semantics over the unit interval [0, 1] with (residuated lattices given by) left-continuous t-norm and a residuated implication, provided tha...