14145609
Functorial semantics for Petri nets under the individual token philosophy
Although the algebraic semantics of place/transition Petri nets under the collective token philosophy has been fully explained in terms of (strictly) symmetric (strict) monoidal categories, the analogous construction under the individual token philosophy is not completely satisfactory because it lacks universality and also functoriality. We introduce the notion of pre-net to recover these aspects, obtaining a fully satisfactory categorical treatment centered on the notion of adjunction. This allows us to present a purely logical description of net behaviours under the individual token philosophy in terms of theories and theory morphisms in partial membership equational logic, yielding a complete match with the theory developed by the authors for the collective token view of nets
15056883
Certifying and Synthesizing Membership Equational Proofs
As the systems we have to specify and verify become larger and more complex, there is a mounting need to combine different tools and decision procedures to accomplish large proof tasks. The problem, then, is how to be sure that we can trust heterogeneous proofs produced by different tools based on different formalisms. In this work we focus on certification and synthesis of equational proofs, that are pervasive in most proof tasks and for which many tools are poorly equipped. Fortunately, equational proof engines like ELAN and Maude can perform millions of equational proof steps per second which, if properly certified, can be trusted by other tools. We present a general method to certify and synthesize proofs in membership equational logic, where the synthesis may involve generating full proofs from proof traces modulo combinations of associativity, commutativity, and identity axioms. We propose a simple representation for proof objects and give algorithms that can synthesize space-efficient, machine-checkable proof objects from proof traces.
7064960
Mapping Modular SOS to Rewriting Logic
Modular SOS (MSOS) is a framework created to improve the modularity of structural operational semantics specifications, a formalism frequently used in the fields of programming languages semantics and process algebras. With the objective of defining formal tools to support the execution and verification of MSOS specifications, we have defined a mapping, named MtoR, from MSOS to rewriting logic (RWL), a logic which has been proposed as a logical and semantic framework. We have proven the correctness of M to R and implemented it as a prototype, the MSOS-SL Interpreter, in the Maude system, a high-performance implementation of RWL. In this paper we characterize the M to R mapping and the MSOS-SL Interpreter. 
 
The reader is assumed to have some basic knowledge of structural operational semantics and object-oriented concepts.
30660022
Semantic Models for Distributed Object Reflection
A generic formal model of distributed object reflection is proposed, that combines logical reflection with a structuring of distributed objects as nested configurations of metaobject that can control subobjects under them. The model provides mathematical models for a good number of existing models of distributed reflection and of reflective middleware. To illustrate the ideas, we show in some detail how two important models of distributed actor reflection can be naturally obtained as special cases of our generic model, and discuss how several recent models of reflective middleware can be likewise formalized as instances of our model.
4862219
Generalized Rewrite Theories
Since its introduction, more than a decade ago, rewriting logic has attracted the interest of both theorists and practitioners, who have contributed in showing its generality as a semantic and logical framework and also as a programming paradigm. The experimentation conducted in these years has suggested that some significant extensions to the original definition of the logic would be very useful in practice. In particular, the Maude system now supports subsorting and conditions in the equational logic for data, and also frozen arguments to block undesired nested rewritings; moreover, it allows equality and membership assertions in rule conditions. In this paper, we give a detailed presentation of the inference rules, model theory, and completeness of such generalized rewrite theories.
720026
Reflective metalogical frameworks
A metalogical framework is a logic with an associated methodology that is used to represent other logics and to reason about their metalogical properties. We propose that logical frameworks can be good metalogical frameworks when their theories always have initial models and they support reflective and parameterized reasoning.We develop this thesis both abstractly and concretely. Abstractly, we formalize our proposal as a set of requirements and explain how any logic satisfying these requirements can be used for metalogical reasoning. Concretely, we present membership equational logic as a particular metalogic that satisfies these requirements. Using membership equational logic, and its realization in the Maude system, we show how reflection can be used for different, nontrivial kinds of formal metatheoretic reasoning. In particular, one can prove metatheorems that relate theories or establish properties of parameterized classes of theories.
27956868
Using Maude