In a similar way as 2-categories can be regarded as a special case of double categories, rewriting logic (in the unconditional case) can be embedded into the more general tile logic, where also side-effects and rewriting synchronization are considered. Since rewriting logic is the semantic basis of several language implementation efforts, it is useful to map tile logic back into rewriting logic in a conservative way, to obtain executable specifications of tile systems. We extend the results of earlier work by two of the authors, focusing on some interesting cases where the mathematical structures representing configurations (i.e., states) and effects (i.e., observable actions) are very similar, in the sense that they have in common some auxiliary structure (e.g., for tupling, projecting, etc.). In particular, we give in full detail the descriptions of two such cases where (net) process-like and usual term structures are employed. Corresponding to these two cases, we introduce two ca...

. 1 Introduction Mapping Tile Logic into Rewriting Logic meseguer@csl.sri.com ugo@di.unipi.it Jos'e Meseguer and Ugo Montanari Rewriting logic [27, 28, 31] extends to concurrent systems with state changes the body of theory developed within the algebraic semantics approach. It can also be Rewriting logic Tile logic membership equational logic 2 double 2VH-categories internal strategies uniform Metodi e Strumenti per la Progettazione e la Verifica di Sistemi Eterogenei Connessi mediante Reti di Comunicazione CONFER2 COORDINA Computer Science Laboratory, SRI International, Menlo Park, Dipartimento di Informatica, Universit`a di Pisa, extends to concurrent systems with state changes the body of theory developed within the algebraic semantics approach. It is both a foundational tool and the kernel language of several implementation efforts (Cafe, ELAN, Maude). extends (unconditional) rewriting logic since it takes into account state changes with side effects and synchronization. It is ...

Abstract. In recent years, several semantics for place/transition Petri nets have been proposed that adopt the collective token philosophy. We investigate distinctions and similarities between three such models, namely configuration structures, concurrent transition systems, and (strictly) symmetric (strict) monoidal categories. Weusethenotionof adjunction to express each connection. We also present a purely logical description of the collective token interpretation of net behaviours in terms of theories and theory morphisms in partial membership equational logic.

. Tile logic extends rewriting logic by taking into account sideeffects and rewriting synchronization. These aspects are very important when we model process calculi, because they allow us to express the dynamic interaction between processes and "the rest of the world". Since rewriting logic is the semantic basis of several language implementation efforts, an executable specification of tile systems can be obtained by mapping tile logic back into rewriting logic, in a conservative way. However, a correct rewriting implementation of tile logic requires the development of a metalayer to control rewritings, i.e., to discard computations that do not correspond to any deduction in tile logic. We show how such methodology can be applied to term tile systems that cover and extend a wide-class of SOS formats for the specification of process calculi. The well-known case-study of full CCS, where the term tile format is needed to deal with recursion (in the form of the replicator operator), is di...

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.

Abstract. To use OWL2 for modeling a system design one must be able to construct a Knowledge Base (KB) that can represent detailed information such as the number of occurrences of a part and interconnections between parts. SysML Block Diagrams (BD) have sufficient expressiveness to represent detailed designs. Suitably restricted SysML block diagrams can be translated into OWL2 to achieve the same result. A SysML graphical syntax can be used for the KBs which are characterized as designs. Block Diagrams have a natural model-theoretic semantic and this semantics is preserved by the translation into OWL2 for a restricted class of Block Diagrams. An implementation of a design is a parts description of the system being modeled. For a design, a KB-model will contain an implementation of the system, but may contain other entities. When additional constraints satisfied by a KB that represents a design then the KB serves as a template for the design implementations. Design KBs can be developed in engineering design tools and exported to OWL tools for analysis. This work yields a partial unification of SysML and OWL that is sufficient for modeling the structure of complex systems.