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"Formal Informal: Inductive Logic and Probabilities" | MCMP joint event with Foundations of Statistics (12 July, 2012)

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On Thursday, 12 July, 2012, the MCMP is meeting the LMU Stats Department once again: The second edition of our series "Formal Informal" will center about "Inductive Logic and Probabilities" this time. Join us for the discussion in an open round at 6:30pm, Alte Bibliothek, room 245 (Ludwigstraße 33). Presenters will be Karine Fradet (Philosophy, Université de Montrèal), Frederik Herzberg (Math. Economics, Bielefeld/MCMP), and Christina Schneider (Philosophy & Statistics, LMU).

From the manifesto: Carnap, who occupies a central place in the development of inductive logic, showed that the disagreements between the interpretation of probabilities as a state of the world and as a state of knowledge of the observer were vain since they were not about the same concept. He concentrated on the second of these two concepts, inductive probabilities, drew the foundations of inductive logic, systematized aspects and approaches, and presented the different methods not as competing against each other, but as part of a system, each perspective being a point on the continuum of the inductive methods.
This edition of Formal Informal will collect, sort, and discuss foundations, applications, and problems of inductive methodology, bridging views from philosophy and statistics.

Download the invitation here as a PDF document.

Algorithmical Aspects of Classical and Philosophical Logic

This 2006 paper (written in German, "Algorithmische Aspekte der klassischen und philosophischen Logik") traces the procedure of automatically treating a given sentence of Natural Language.

Abstract

This paper presents various aspects of the use of algorithms in propositional and first order logic. The history of logic automata and of the notion ‘algorithm’ itself is outlined in the first chapter—followed by the declaration of the pseudo code notation used for presenting different implementations in the text. The next chapters follow the process of treating a given natural language proposition with automated procedures. Chapter 2 discusses a symbolization strategy suggested by Godehard Link in Collegium Logicum—Logische Grundlagen der Philosophie [Link 2003] (enclosed as appendix A), especially with respect to the so called “donkey sentences” and their treatment in Discourse Representation Theory. The subject of chapter 3 is the conversion of first order formulas into Prenex Normal Form. Here an algorithm for PNF conversion on the basis of tree structures is established and a graphical implementation in the object oriented programming language Java is discussed. Chapter 4 gives an overview over applied automated proof
strategies, especially with regard to Herbrand’s Theorem. The paper concludes with the discussion of an algorithm as decision procedure for propositional formulas, the Quine Analysis, as described in [Link 2003].

Keywords

Automata, Algorithms, Formalization of Natural Language, Prenex Normal Form Conversion (implemented), Tree Representation of Formulae, Herbrand Expansion, Tableaux with Unification, Skolemization, Quine Analysis (implemented)

Supplement

The paper was originally intended to be supplemented with a CD-Rom containing graphical implementations of PNF conversion (chpt. 3) and Quine Analysis (chpt. 5) as a platform-independent Java program that utilizes tree structures for analyzing and manipulating formulas. The program can now be found online as Logics Pack Console. Selected code blocks are shown in print in appendix D.

Download

Download as PDF (~3MB)

Teddy Seidenfeld at the MCMP & Statistics Department joint event, 29 July 2011

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Teddy Seidenfeld (Carnegie Mellon University, Pittsburgh) will give a talk at the joint event of the Research Seminar on Foundations of Statistics (LMU Statistics Department) and the MCMP Colloquium titled "Three contrasts between two senses of coherence" (organization: Roland Poellinger). The talk will take place on 29 July, 15 c.t., after coffee and cake at 14:30 in the "Alte Bibliothek" of the statistics department (Ludwigstr. 33, room 245). Download the invitation with the abstract as a PDF here and find the slides of the talk on Teddy Seidenfeld's website here!

Logics Pack Console

logicspackWith this Java WebStart application formulae of first order logic (e.g., in accordance with the inductive definition in G. Link: Collegium Logicum) may be transformed into their equivalent prenex form (in compliance with the rules of Kalish, Montague, Mar: Techniques of Formal Reasoning, p. 427 ff.), and formulae of propositional logic may be checked with "Quine Analysis". The console is based on a formula parser that generates the appropriate tree structure for each input formula. Every formula transformation is conducted on the underlying tree structure. An additional feature of the program is the graph display for the visualization of the generated trees and the animation of the prenex algorithm.

In the graph window use left click and drag in the graph pane to navigate and right click with horizontal mouse movement for zooming.

Please note that for the execution of this unsigned WebStart application a security exception must be added to your local settings.

Open logics pack console | Check your local Java installation