We present a novel approach based on inductive theorem proving for verifying invariants of dynamic systems specified in rewriting logic, a formal specification language implemented in the Maude system. An invariant is a property that holds on all the states that are reachable from a given class of initial states. Our approach consists in encoding the semantic aspects that are relevant for our t...

As a computer science application of our techniques we may take the action logic of [Pratt, 1990]. Action logic is a finitely based equational theory conservatively extending the equational theory of regular expressions. An action algebra (model of action logic) is implicitly partially ordered via a ≤ b just when a + b = b . However a + b plays no other essential role in action logic, and may b...

We present an approach based on inductive theorem proving for verifying invariants of dynamic systems specified in rewriting logic, a formal specification language implemented in the Maude system. An invariant is a property that holds on all the states that are reachable from a given class of initial states. Our approach consists in encoding the semantic aspects that are relevant for our task (...

Names, or object-level variables, are a ubiquitous feature in programming languages and other computational applications. Reasoning with names, and related constructs like binding and freshness, often poses conceptual and technical challenges. Nominal Equational Logic (NEL) is a logic for reasoning about equations in the presence of freshness side conditions. This paper gives a category theoret...

Declarative debugging is a semi-automatic technique that starts from an incorrect computation and locates a program fragment responsible for the error by building a tree representing this computation and guiding the user through it to find the error. Membership equational logic (MEL) is an equational logic that in addition to equations allows to state of membership axioms characterizing the ele...

Many formal systems, particularly in computer science, may be captured by equations modulated by side conditions asserting the “freshness of names”; these can be reasoned about with Nominal Equational Logic (NEL). Like most logics of this sort NEL employs this notion of freshness as a first class logical connective. However, this can become inconvenient when attempting to translate results from...

We give a notation and a logical calculus for the description and deductive manipulation of dynamic networks of communicating components. We represent such nets by hierarchical systems of recursive equations for streams. We give logical rules that describe the communication within a net and the dynamic creation of components, channels and rearrangement of the net structure. Such net transformat...

Appetizer. Algebraic logic (AL) is a well established discipline yet some natural questions remain out of its scope. For instance, it is well known that the Horn and universal fragments of FOL are original logics close to equational logic rather than just sublogics of FOL, and, very similarly, Gentzen's axiomatization of FOL seems has much in common with the universal equational logic: how c a ...

Recently, three approaches to deductive planning were developed, which solve the technical frame problem without the need to state frame axioms explicitly. These approaches are based on the linear connection method, an equational Horn logic, and linear logic. At rst glance these approaches seem to be very diierent. In the linear connection method a syntactical condition | each literal is connec...

In this paper we describe collaborative constraint functional logic programming and the system called Open CFLP that supports this programming paradigm. The system solves equations by collaboration of various equational constraint solvers. The solvers include higher-order lazy narrowing calculi that serve as the interpreter of higher-order functional logic programming, and specialized solvers f...