Model Theory

A simplified framework for first-order languages and its formalization in Mizar

by Marco Caminati

A geometric introduction to forking and thorn-forking

by Adler Hans

Thorn-forking as local forking

by Adler Hans

An introduction to theories without the independence property

by Adler Hans

Empirical Adequacy and Ramsification

by Jeffrey Ketland

BJPS 2004

Structural realism has been proposed as an epistemological position interpolating between realism and sceptical... more Structural realism has been proposed as an epistemological position interpolating between realism and sceptical anti-realism about scientific theories. The structural realist who accepts a scientific theory T thinks that T is empirically correct, and furthermore is a realist about the ‘structural content’ of T. But what exactly is ‘structural content’? One proposal is that the ‘structural content’ of a scientific theory may be associated with its Ramsey sentence Ram(T). However, Demopoulos and Friedman argued, using ideas drawn from Newman’s earlier criticism of Russell’s structuralism, that this move fails to achieve an interesting intermediate position between realism and anti-realism. Rather, Ram(T) adds little content beyond the instrumentalistically acceptable claim that the theory T is empirically adequate.

Here, we formulate carefully the crucial claim of Demopoulos and Friedman, and show that the Ramsey sentence Ram(T) is true just in case T possesses a full model which is empirically correct and satisfies a certain cardinality condition on its theoretical domain. This suggests that structural realism is not a position significantly different from the anti-realism it attempts to distinguish itself from.

The logic of sheaves, sheaf forcing and the independence of the Continuum Hypothesis

by J. Benavides

An introduction is given to the logic of sheaves of structures and to set theoretic forcing constructions based on... more An introduction is given to the logic of sheaves of structures and to set theoretic forcing constructions based on this logic. Using these tools, it is presented an alternative proof of the independence of the Continuum Hypothesis; which simplifies and unifies the classical boolean and intuitionistic approaches, avoiding the difficulties linked to the categorical machinery of the topoi based approach.

Sheaf Logic, Quantum Set Theory and the Interpretation of Quantum Mechanics.

by J. Benavides

Based on the Sheaf Logic approach to set theoretic forcing, a hierarchy of Quantum Variable Sets is constructed, which... more Based on the Sheaf Logic approach to set theoretic forcing, a hierarchy of Quantum Variable Sets is constructed, which generalizes and simplifies the analogous construction developed by Takeuti on boolean valued models of set theory. Over this model, two alternative proofs of Takeuti’s correspondence, between self adjoint operators and the real numbers of the model, are given. This approach results to be more constructive, showing a direct relation with the Gelfand representation theorem, and revealing also the importance of these results with respect to the interpretation of Quantum Mechanics in close connection with the Deutsch-Everett multiversal interpretation of quantum theory. Finally, it is shown how in this context the notion of genericity and the corresponding generic model theorem can help to explain the emergence of classicality in Quantum Mechanics also in close connection with the Deutsch-Everett perspective.

Tarski’s undefinability theorem. Very short introduction. Version 1.2

by Bartosz Janik

draft

The Evolution of Cable Regulatory Policies and Their Impact: A Comparison of South Korea and Israel

by Amit Schejter

Nonstandard Algebraic Models for Fuzzy Logics

by Lorenzo Peña

On the Interpretation of the Propositional Calculus

by Tristan Haze

A fairly polished draft

The question considered is 'How can formulae of the propositional calculus be brought into a representational relation... more The question considered is 'How can formulae of the propositional calculus be brought into a representational relation with the world?'. Four approaches are discussed: (1) the denotational approach, on which formulae are taken to denote objects, (2) the abbreviational approach, on which formulae and connectives are taken to abbreviate natural-language expressions, (3) the truth-conditional approach, on which truth-conditions are stipulated for formulae, and (4) the modelling approach, on which formulae, together with either valuation- or proof-theory, are regarded as an abstract structure capable of bearing (via stipulation) a representational relation to the world.

The modelling approach is developed here for the first time. The simple technical apparatus used for this is then applied to two issues in the philosophy of logic. (1) I demonstrate a corollary or converse to Carnap's result that certain 'non-normal' valuation-functions can be added to the set of admissible valuations of formulae without destroying the soundness and completeness of standard proof-theories. This sheds considerable light on a recent thread of the inferentialism debate which involves dialectical use of Carnap's result. (2) I show how the approach can be extended to quantification theory, by defining a model-theoretic notion of validity equivalent to the usual one, but making use of a proof-theoretic apparatus in place of the device of assigning values to formulae. This sheds light on the close relationship between proof- and valuation-theory.

Equivalence Relations & Topological Automorphism Groups In Simple Theories

by Aviv Keren

M.Sc. Thesis

Skolem Functions and Herbrand Universes In a Tree Generalization of First Order Logic

by Sylvain Hallé

Roger Villemaire, Sylvain Hallé, Omar Cherkaoui. (2006). Proceedings of the 5th Mexican International Conference on Artificial Intelligence (MICAI 2006), IEEE Computer Society, 22-31.

Skolem functions and Herbrand universes are fundamental concepts in first-order logic that form the basis of many... more Skolem functions and Herbrand universes are fundamental concepts in first-order logic that form the basis of many works in artificial intelligence. In this paper, we study a fragment of the XML Query Language (XQuery) that generalizes first-order logic to a setting where variables form a forest instead of a set. A formal description of the logic and its semantics is given; Skolem functions and Herbrand universes are generalized to this setting.