Analytic Methods for the Logic of Proofs

The logic of proofs (lp) was proposed as Gdels missed link between Intuitionistic and S4-proofs, but so far the tableau-based methods proposed for lp have not explored this closeness with S4 and contain rules whose analycity is not immediately evident. We study possible formulations of analytic tableau proof methods for lp that preserve the subformula property. Two sound and complete tableau decision methods of increasing degree of analycity are proposed, KELP and preKELP. The latter is particularly inspired on S4-proofs. The crucial role of proof constants in the structure of lp-proofs methods is analysed. In particular, a method for the abduction of proof constant specifications in strongly analytic preKELP proofs is presented; abduction heuristics and the complexity of the method are discussed.

A Note on the Use of Sum in the Logic of Proofs

The Logic of Proofs~LP, introduced by Artemov, encodes the same reasoning as the modal logic~S4 using proofs explicitly present in the language. In particular, Artemov showed that three operations on proofs (application~$\cdot$, positive introspection~!, and sum~+) are sufficient to mimic provability concealed in S4~modality. While the first two operations go back to G{\"o}del, the exact role of~+ remained somewhat unclear. In particular, it was not known whether the other two operations are sufficient by themselves. We provide a positive answer to this question under a very weak restriction on the axiomatization of LP.

Visualizing a logic of dependability arguments

This paper offers general guidelines for the development of effective visual languages. That is, languages for constructing diagrams that can be easily and readily interpreted and manipulated by the human reader. We use these guidelines first to examine classical AND/OR trees as a representation of logical proofs, and second to design and evaluate a visual language for representing proofs in LofA: a Logic of Dependability Arguments, for which we provide a brief motivation and overview.

The Decision on Turkish EU accession in December 2002: The logic of anarchy, collective action problems and rhetorical action

Studies of the EU accession of the East and Central European Countries have stressed the importance of neo-liberal institutionalism as an explanation for Member State preferences. In this paper it is argued that Member States’ preferences over Turkish EU accession are better explained by power politics and neo-realism. It seems therefore that Turkey’s way to the EU follows another path than the East and Central Countries. Turkish accession raises the question of the EU’s role in a uni-polar world order – whether the EU should develop into an independent actor on the world stage or not. However, when it comes to the interaction among the Member States in order to decide on when to open accession negotiations with Turkey the constitutive values of the EU seriously modify the outcome that pure power politics would have let to.

Classificações de signos de C.S.Peirce: de ‘On the Logic of Science’ ao ‘Syllabus of Certain Topics of Logic’

As classificações dos signos de C.S.Peirce começam a ser desenvolvidas em 1865 e se estendem a até, pelo menos, 1909. Vou apresentar o período que tem início em 1865, e possui dois momentos de intensa produção - "On a New List of Categories" e "On the Algebra of Logic: a contribution to the philosophy of notation". Em seguida apresento as dez classes de signos, uma morfologia que aparece no "Syllabus of Certain Topics of Logic", e é desenvolvida a partir de 1903. Meu propósito aqui é familiarizar o leitor com as intrincadas classificações sígnicas de Peirce.