A higher-order behavioural algebraic institution for ASL

In this paper, we generalise the semantics of ASL including the three behavioural operators for a fixed but arbitrary algebraic institution. After that, we define a behavioural algebraic institution which is used to give an alternative semantics of the behavioural operators, to define the normal forms of the both semantics of behavioural operators and to relate both semantics. Finally, we present a higher-order behavioural algebraic institution.Postprint (published version

Finitary non-compositional proof systems for ASL in first-order

In this paper we present finitary proof systems for the deduction of sentences from algebraic specifications inductively defined by specification expresssions in first-order and higher-order logic. Mainly, we redesign the proof systems for the reachability and behavioural operators. The main application of the result is to give an adequate representation of this kind of proof systems in a type-theoretic logical framework.Postprint (published version

A Logic for Non-Deterministic Parallel Abstract State Machines

We develop a logic which enables reasoning about single steps of non-deterministic parallel Abstract State Machines (ASMs). Our logic builds upon the unifying logic introduced by Nanchen and St\"ark for reasoning about hierarchical (parallel) ASMs. Our main contribution to this regard is the handling of non-determinism (both bounded and unbounded) within the logical formalism. Moreover, we do this without sacrificing the completeness of the logic for statements about single steps of non-deterministic parallel ASMs, such as invariants of rules, consistency conditions for rules, or step-by-step equivalence of rules.Comment: arXiv admin note: substantial text overlap with arXiv:1602.0748

The Universal Theory of First Order Algebras and Various Reducts

First order formulas in a relational signature can be considered as operations on the relations of an underlying set, giving rise to multisorted algebras we call first order algebras. We present universal axioms so that an algebra satisfies the axioms iff it embeds into a first order algebra. Importantly, our argument is modular and also works for, e.g., the positive existential algebras (where we restrict attention to the positive existential formulas) and the quantifier-free algebras. We also explain the relationship to theories, and indicate how to add in function symbols.Comment: 30 page