Abstract
Deduction systems and graph transformation systems are compared within a common categorical framework. This comparison results in a proposal for a new deduction method in diagrammatic logics, allowing the deletion of intermediate lemmas.
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Corradini, A., Montanari, U., Rossi, F., Ehrig, H., Heckel, R., Löwe, M.: Algebraic approaches to graph transformation—part I: basic concepts and double pushout approach. In: Handbook of Graph Grammars and Computing by Graph Transformation, vol. 1. Foundations, World Scientific, pp. 163–246 (1997)
Corradini A., Heindel T., Hermann F., König B.: Sesqui-Pushout transformation. International Conference on Graph Transformations (ICGT 2006). Lect. Notes Comput. Sci. 4178, 30–45 (2006)
Domínguez C., Duval D.: Diagrammatic logic applied to a parameterization process. Math. Struct. Comput. Sci. 20(4), 639–654 (2010)
Dumas J.-G., Duval D., Reynaud J.-C.: Cartesian effect categories are Freyd-categories. J. Symbol. Comput. 46(3), 272–293 (2011)
Dumas J.-G., Duval D., Fousse L., Reynaud J.-C.: A duality between exceptions and states. Math. Struct. Comput. Sci. 22(4), 719–722 (2012)
Dumas J.-G., Duval D., Fousse L., Reynaud J.-C.: Decorated proofs for computational effects: States. Applied and Computational Category Theory (ACCAT 2012). Electron. Proc. Theoret. Comput. Sci. 93, 45–59 (2012)
Duval D.: Diagrammatic specifications. Math. Struct. Comput. Sci. 13, 857–890 (2003)
Duval D., Echahed R., Prost F.: Graph transformation with focus on incident edges. International Conference on Graph Transformations (ICGT 2012). Lect. Notes Comput. Sci. 7562, 156–171 (2012)
Dyckhoff R., Tholen W.: Exponentiable morphisms, partial products and pullback complements. J. Pure Appl. Algebra 49(1–2), 103–116 (1987)
Ehrig, H., Heckel, R., Korff, M., Löwe, M., Ribeiro, L., Wagner, A., Corradini, A.: Algebraic Approaches to Graph Transformation—part II: Single Pushout Approach and Comparison with Double Pushout Approach. In: Handbook of Graph Grammars and Computing by Graph Transformation, vol. 1. Foundations, World Scientific, pp. 247–312 (1997)
Goguen J.A., Burstall R.M.: Introducing Institutions. Lect. Notes Comput. Sci. 164, 221–256 (1984)
Heindel, T., Sobocinski, P.: Being Van Kampen is a universal property. Logic. Methods Comput. Sci. 7(1) (2011)
Lambek J.: Deductive systems and categories I. Math. Syst. Theory 2(4), 287–318 (1968)
Lawvere, F.W.: Adjointness in foundations, vol. 23, pp. 281–296 (1969). (Republished in: Reprints Theory Appl. Categor. 16, 1–16 (2006))
Löwe, M.: Graph rewriting in span-categories. International Conference on Graph Transformations (ICGT 2010). In: Lect. Notes Comput. Sci. 6372, 218–233 (2010)
Löwe M.: Refined graph rewriting in span-categories—a framework for algebraic graph transformation. International Conference on Graph Transformations (ICGT 2012). Lect. Notes Comput. Sci. 7562, 111–125 (2012)
Monserrat, M., Rosselló, F., Torrens, J., Valiente, G.: Single pushout rewriting in categories of spans I: the general setting. Technical Report LSI-97-23-R, Departament de Llenguatges i Sistemes Inform‘atics, Universitat Polit‘ecnica de Catalunya (1997)
Mossakowski, T., Goguen, J., Diaconescu, R., Tarlecki, A.: What is a Logic? (revised version) Logica Universalis, pp. 111–133 (2007)
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This work has been funded by the project CLIMT of the French Agence Nationale de la Recherche (ANR-11-BS02-016).
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Duval, D. Deduction as Reduction, from a Categorical Point of View. Log. Univers. 7, 275–289 (2013). https://doi.org/10.1007/s11787-013-0082-0
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DOI: https://doi.org/10.1007/s11787-013-0082-0