Observation and abstract behaviour in specification and implementation of state-based systems

Classical algebraic specification is an accepted framework for specification. A criticism which applies is the fact that it is functional, not based on a notion of state as most software development and implementation languages are. We formalise the idea of a state-based object or abstract machine using algebraic means. In contrast to similar approaches we consider dynamic logic instead of equational logic as the framework for specification and implementation. The advantage is a more expressive language allowing us to specify safety and liveness conditions. It also allows a clearer distinction of functional and state-based parts which require different treatment in order to achieve behavioural abstraction when necessary. We shall in particular focus on abstract behaviour and observation. A behavioural notion of satisfaction for state-elements is needed in order to abstract from irrelevant details of the state realisation

Note on paraconsistency and reasoning about fractions

We apply a paraconsistent logic to reason about fractions.Comment: 6 page

A graph-theoretic account of logics

A graph-theoretic account of logics is explored based on the general notion of m-graph (that is, a graph where each edge can have a finite sequence of nodes as source). Signatures, interpretation structures and deduction systems are seen as m-graphs. After defining a category freely generated by a m-graph, formulas and expressions in general can be seen as morphisms. Moreover, derivations involving rule instantiation are also morphisms. Soundness and completeness theorems are proved. As a consequence of the generality of the approach our results apply to very different logics encompassing, among others, substructural logics as well as logics with nondeterministic semantics, and subsume all logics endowed with an algebraic semantics

Refinement by interpretation in {\pi}-institutions

The paper discusses the role of interpretations, understood as multifunctions that preserve and reflect logical consequence, as refinement witnesses in the general setting of pi-institutions. This leads to a smooth generalization of the refinement-by-interpretation approach, recently introduced by the authors in more specific contexts. As a second, yet related contribution a basis is provided to build up a refinement calculus of structured specifications in and across arbitrary pi-institutions.Comment: In Proceedings Refine 2011, arXiv:1106.348

Poly-infix operators and operator families

Poly-infix operators and operator families are introduced as an alternative for working modulo associativity and the corresponding bracket deletion convention. Poly-infix operators represent the basic intuition of repetitively connecting an ordered sequence of entities with the same connecting primitive.Comment: 8 page

Hilbert-Post completeness for the state and the exception effects

In this paper, we present a novel framework for studying the syntactic completeness of computational effects and we apply it to the exception effect. When applied to the states effect, our framework can be seen as a generalization of Pretnar's work on this subject. We first introduce a relative notion of Hilbert-Post completeness, well-suited to the composition of effects. Then we prove that the exception effect is relatively Hilbert-Post complete, as well as the "core" language which may be used for implementing it; these proofs have been formalized and checked with the proof assistant Coq.Comment: Siegfried Rump (Hamburg University of Technology), Chee Yap (Courant Institute, NYU). Sixth International Conference on Mathematical Aspects of Computer and Information Sciences , Nov 2015, Berlin, Germany. 2015, LNC