Proceedings of the Conference on Hypothetical Reasoning, 23-24 August 2014, Tübingen

Hypothetical reasoning or reasoning under assumptions is a key concept of logic, philosophy of science and mathematics. The Conference on Hypothetical Reasoning focussed on its logical aspects, such as assumption-based calculi and their proof theory, logical consequence from a proof-theoretic or model-theoretic point of view, logics of conditionals, proof systems, structure of assumption-based proofs, hypotheses in proof-theoretic semantics, notions of implication, substructural logics, hypotheses in categorial logic, logical aspects of scientific explanation, hypothetical reasoning in mathematics and reasoning from definitions and axioms. The conference took place 23–24 August, 2014 in Tübingen at the Department of Philosophy, in conjunction with ESSLLI 2014. The proceedings collect abstracts, slides and papers of the presentations given

On the strength of dependent products in the type theory of Martin-L\"of

One may formulate the dependent product types of Martin-L\"of type theory either in terms of abstraction and application operators like those for the lambda-calculus; or in terms of introduction and elimination rules like those for the other constructors of type theory. It is known that the latter rules are at least as strong as the former: we show that they are in fact strictly stronger. We also show, in the presence of the identity types, that the elimination rule for dependent products--which is a "higher-order" inference rule in the sense of Schroeder-Heister--can be reformulated in a first-order manner. Finally, we consider the principle of function extensionality in type theory, which asserts that two elements of a dependent product type which are pointwise propositionally equal, are themselves propositionally equal. We demonstrate that the usual formulation of this principle fails to verify a number of very natural propositional equalities; and suggest an alternative formulation which rectifies this deficiency.Comment: 18 pages; v2: final journal versio

Untersuchungen zur regellogischen Deutung von Aussagenverknüpfungen (Dissertation Universität Bonn 1981)

As certain aspects of my doctoral dissertation of 1981 are still being discussed, I re- publish it here as an online resource in its original German form. It introduces the notion of rules of higher levels in order to give a general schema for the characterization of logical connectives in terms of rules. It also makes a proposal for a treatment of negation on the basis of a denial operator. It thus deals with core issues of proof-theoretic semantics. The German dissertation is accompanied by an English manuscript "Sentential Calculi with Rules of Arbitrary Levels" which gives a summary of central ideas and results of Chapters 1 and 2 of the dissertation

Ein Logik-Lotse geht von Bord. Zur Verabschiedung des Naturwissenschaftlers und Philosophen Walter Hoering

Würdigung von Prof. Dr. Dr. Walter Hoering anlässlich seines Ausscheidens aus dem aktiven Dienst an der Universität Tübingen

Proof-theoretic Validity Based on Elimination Rules

In the tradition of Dummett-Prawitz-style proof-theoretic semantics, which considers validity of derivations or proofs as one of its core notions, this paper sketches an approach to proof-theoretic validity based on elimination rules and assesses its merits and limitations. Some remarks are made on alternative approaches based on the idea of dualizing connectives and proofs, as well as on definitional reflection using elimination clauses

Walter Felscher (1931-2000). Nachruf

In den Tübinger Universitätsnachrichten (9. April 2001, Jahrgang 21, Nr. 100) erschienener Nachruf auf Prof. Dr. Walter Felsche

Preface

The 14th International Congress of Logic, Methodology and Philosophy of Science was held in July, 19th – 26th, 2011 in Nancy, the historic capital of Lorraine and birthplace of Henri Poincaré. We were very honored that the President of the French Republic, Monsieur Nicolas Sarkozy, generously agreed his patronage. The LMPS congresses represent the current state of the art and offer new perspectives in its fields. There were 900 registered participants from 56 different countries. They filled ..