Sesión extraordinaria del Seminario (19/02/2018): Daniele Chiffi

Sesión extraordinaria del Seminario Lógica y Lenguaje
19 de Febrero 2018, 11:00h
Aula de Grados
Facultad de Filosofía
Universidad de Sevilla

Dr. Daniele Chiffi
Research Fellow at Tallinn University of Technology

Logical Inference in the Diagrammatic System of Assertive Graphs

The notion of assertion plays an inferential role in logic. It is a key ingredient in most logical systems, either implicitly or explicitly. For instance, Frege’s ideographical language of the Begriffsschrift introduced a specific sign designating assertion, ‘⊢’, which expresses the acknowledgement of the truth of the content of the assertion. In Peirce’s graphical logic of Existential Graphs (EGs), there is no specific sign for assertion, although the notion of assertion is used virtually everywhere in his logical writings. The reason is that making an assertion signals the responsibility that the utterer of the logical statement bears on the truth of the proposition [1]. Indeed Peirce has assertion as a sign that is embedded in the Sheet of Assertion (SA) [2], while SA represents both the logical truth as well as the assertoric nature of those graphical logical formulas that are scribed upon it. In intuitionistic logic, on the other hand, an explicit notion of assertion has been used in order to analyse inference and proof, to explicate the meaning of logical constants, and so on [3; 4]. The idea of the notion of assertion thus appears robustly invariant across a range of logical theories, logical methods, and logical notations. In the light of the existence of such a common and shared character of assertions, we present a new system of graphs that makes the embedded or implicit nature of assertions in logical graphs explicit. We develop a graphical logic of assertions (called “Assertive Graphs”, (AGs))[5, 6]. We will show that it is possible to extend this constructive logic of AGs into a classical graphical logic ClAG without a need to introduce polarities in the graphs. We compare the advantages of these two approaches and point out the nature of a deep inference of their transformation rules. Finally, we discuss implications of AGs to logical inference.