# José David García Cruz

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##### Opposition Relations Between Prophecies with Yessica Espinoza Ramos In Linker S. Corter J. Giardino V. Bosveld-de Smet L. Chapman P. Pietarinen Av (ed.), Diagrammatic Representation and Inference. Diagrams 2020. Lecture Notes in Computer Science, . pp. 394-401. 2020.
This paper presents two versions of opposition relations for prophetical statements, the first one is an application of “Ockham’s thesis” in Classical propositional Logic. The second one is a reinterpretation of that thesis in the logic MRSP.
• ##### Aristotelian Relations in PDL: The Hypercube of Dynamic Oppositions Special Issue 5th World Congress on the Square of Opposition Easter Island, November 11-15, 2016. 2017.
The aim of this paper is to study aristotelian relation in an extension of Propositional Dynamic Logic, the logic PDLQ+(¬). The main result of our study is the production of a geometrical opposition structure called hypercube of Dynamic Opposition, this structure is very useful to study negation of atomic programs and dynamic modalities.
•  53
##### A Modal Logic to Reason about Analogical Proportion Studia Metodologiczne 37 (1): 73-96. 2016.
A modal logic for representing analogical proportions is presented. This logic is a modal interpretation of H. Prade and G. Richard's homogeneous analogy. A tableaux system is given with some examples an intuitions.
•  3
##### From the Square to Octahedra In Jean-Yves Beziau & Gianfranco Basti (eds.), The Square of Opposition: A Cornerstone of Thought. pp. 253-272. 2017.
Colwyn Williamson (Notre Dame J. Formal Log. 13:497–500, 1972) develops a comparison between propositional and syllogistic logic. He outlines an interpretation of the traditional square of opposition in terms of propositional logic, that is, the statements corresponding to the corners of the traditional square can be represented with propositional logic operators. His goal is to present a twofold square that preserves the truth conditions of the relationships between the formulas, and define oth…Read more