R. Bruni, J. Meseguer, and U. Montanari. Symmetric monoidal and cartesian double categories as a semantic framework for tile logic. Mathematical Structures in Computer Science, 2000. To appear.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....of the elements in each of the three dimensions and by xing their interplay. In fact, several contributions to the semantic foundation of Tile Logic and its application to Computer Supported Cooperative Work have been developed that allow to investigate di erent features and properties. In [BMM02] two classes of Tile Logic are considered, called Process Tile Logic (PTL) and Term Tile Logic (TTL) where the horizontal structure is completely analogous to the vertical structure and consists of a special kind of acyclic graphs in the case of PTL and of ordinary terms in the case of TTL. ....

R. Bruni, J. Meseguer, and U. Montanari. Symmetric monoidal and cartesian double categories as a semantic framework for tile logic. Mathematical Structures in Computer Science, 12(1):53{ 90, 2002.

No context found.

R. Bruni, J. Meseguer, and U. Montanari. Symmetric monoidal and cartesian double categories as a semantic framework for tile logic. Mathematical Structures in Computer Science, 2000. To appear.

.... tiles can be added for free, which guarantee the consistency between the adjoined structure (e.g. symmetries or cartesianity) and the categorical models for such systems must be taken in the corresponding categories of, e.g. symmetric monoidal double categories or cartesian double categories [9, 4]. Fixing the auxiliary tiles and the format of the basic tiles of the system means xing a tile format. Several ( rst order) tile formats have been e.g. de ned which guarantee that tile bisimilarity is a congruence [5] they usually exploit the format independent tile decomposition property ....

Bruni, R., J. Meseguer and U. Montanari, Symmetric monoidal and cartesian double categories as a semantic framework for tile logic, Math. Struct. in Comput. Sci. (2001), to appear.

.... tiles can be added for free, which guarantee the consistency between the adjoined structure (e.g. symmetries or cartesianity) and the categorical models for such systems must be taken in the corresponding categories of, e.g. symmetric monoidal double categories or cartesian double categories [9, 4]. Fixing the auxiliary tiles and the format of the basic tiles of the system means fixing a tile format . Several (first order) tile formats have been e.g. defined which guarantee that tile bisimilarity is a congruence [ 5] they usually exploit the format independent tile decomposition property ....

Bruni, R., J. Meseguer and U. Montanari, Symmetric monoidal and cartesian double categories as a semantic framework for tile logic, Math. Struct. in Comput. Sci. (2001), to appear.

No context found.

Roberto Bruni, Jos'e Meseguer, and Ugo Montanari. Symmetric monoidal and cartesian double categories as a semantic framework for tile logic. Mathematical Structures in Computer Science, 2000. To appear.

.... (monoidal) categories in a very elementary way, i.e. just for representing terms and substitutions diagrammatically as abstract arrows (from the arguments to the result) In particular we shall consider neither the categorical models of tile logic (expressed by suitable monoidal double categories [25, 10]) nor the axiomatized proof terms decorating tile sequents [25, 8] Varying the algebraic structure of configurations and observations, tiles can model many different aspects of dynamic systems, ranging from synchronization of Petri net transitions [12] to causal dependencies for located calculi ....

....over a signature. Namely, 1) the monoidal tile format [32] which has monoidal structures of both configurations and observations; 2) the algebraic tile format [25] which has a cartesian structure of configurations but only a monoidal structure of observations; and (3) the term tile format [10, 8], which has cartesian configurations and observations. Although none of them ensures that tile bisimilarity is a congruence, by restricting these formats to satisfy the so called basic source property (see [25, 4] one can easily recover either the De Simone, or the positive gsos, or the zyft ....

R. Bruni, J. Meseguer, and U. Montanari. Symmetric monoidal and cartesian double categories as a semantic framework for tile logic. Math. Struct. in Comput. Sci., 2001. To appear.

.... (monoidal) categories in a very elementary way, i.e. just for representing terms and substitution diagrammatically as abstract arrows (from the arguments to the result) In particular we shall consider neither the categorical models of tile logic (expressed by suitable monoidal double categories [12,6]) nor the axiomatized proof terms decorating tile sequents. Varying the algebraic structure of con gurations and observations tiles can model many di erent aspects of dynamic systems, ranging from synchronization of net transitions [7] to causal dependencies for located calculi and nitely ....

....over a signature. Namely, 1) the monoidal tile format [17] which has monoidal structures of both con gurations and observations; 2) the algebraic tile format [12] which has a cartesian structure of con gurations but only a monoidal structure of observations; and (3) the term tile format [6,4], which has cartesian structures of both con gurations and observations. Although none of them ensures that tile bisimilarity is a congruence, by restricting these formats one can easily recover either the De Simone, or the positive gsos, or the zyft format. Here, we shall focus only on the ....

R. Bruni, J. Meseguer, and U. Montanari. Symmetric monoidal and cartesian double categories as a semantic framework for tile logic. Mathematical Structures in Computer Science, 2000. To appear.

.... on three tile formats where con gurations and observations re ects the approaches linearity, free duplication and explicit sharing previously discussed: 1) the monoidal tile format (mtf) 18] whose con gurations and observations have a monoidal structure; 2) the term tile format (ttf) [5,6], whose con gurations and observations have a cartesian structure; 3) the gs monoidal tile format (gstf) whose con gurations have a gs monoidal structure and observations have a monoidal structure. The mtf corresponds to abandoning sharing of subterms in con gurations. The ttf extends the ....

R. Bruni, J. Meseguer, and U. Montanari. Symmetric monoidal and cartesian double categories as a semantic framework for tile logic. Mathematical Structures in Computer Science, 1999. To appear.

....to the tile rewrite system [26] Additional operations and axioms can be imposed on proof terms, configurations and observations whenever extra structure is required. Correspondingly, tile models are enriched and the construction of the initial models adapted. Symmetric monoidal, cartesian [3] and cartesian closed versions [4] of tiles have been defined. Moreover, different structures for configurations, observations and proof terms can be introduced to tailor the logic and the models to the specific needs of the applications. An expressive specification language for this purpose is ....

R. Bruni, J. Meseguer and U. Montanari, Symmetric Monoidal and Cartesian Double Categories as a Semantic Framework for Tile Logic, to appear in MSCS.

....steps) to generate larger steps. Thanks to these composition properties, there exists a precise correspondence between tiles and the cells of suitable double categories. While the interpretation of tiles as double cells is already described in [9] in previous joint work with Jose Meseguer [3, 5] and in the PhD thesis of one of the authors [2] a precise categorical formulation is given for those tile systems whose configurations and observations rely on the same algebraic structure (e.g. symmetric monoidal or cartesian) The categorical models for such systems have been defined in terms ....

....two appendices have also been included. In Appendix A both the syntax and the categorical interpretation of simply typed calculus are briefly discussed. Hopefully, this should help to see the analogy with the bidimensional structures that we consider. In Appendix B, we recall from [5] the axiomatization of (canonical) cartesian double categories. 2. Background We review some basics on cartesian closed categories that can be useful to see the analogy with their corresponding bidimensional versions in the theory of double categories. Since double categories might be unfamiliar ....

[Article contains additional citation context not shown here]

R. Bruni, J. Meseguer, and U. Montanari. Symmetric monoidal and cartesian double categories as a semantic framework for tile logic. Mathematical Structures in Computer Science, 1999. To appear.

No context found.

R. Bruni, J. Meseguer, and U. Montanari. Symmetric monoidal and cartesian double categories as a semantic framework for tile logic. Mathematical Structures in Computer Science, 12(1):53-90, 2002.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC