DFOL is a logic that extends first-order logic with dependent types. We give a translation from DFOL to FOL formalized as an institution comorphism and show that it admits the model expansion property. This property together with the borrowing theorem implies the soundness of borrowing — a result that enables us to reason about entailment in DFOL by using automated tools for FOL. In addition, t...

We argue that logic is not a uniform terrain where all truths lie on a par. We analyze the apparatus of first-order classical logic with identity into two main ingredients: a deeper and wider component and, on top of it, a narrower component which consists of principles that articulate our modern notion of object.

We construct Abelian group with an extra structure whose first order theory has finitely many but more than one countable model.

I’m writing these remarks on the occasion of the AIM workshop on model theory for metric structures that Itäı Ben-Yaacov and I are organizing for the week Sept. 18–22, 2006. This is the first research meeting in which the new continuous version of first-order logic takes center stage for discussions about making model theory an effective tool in analysis, probability, and geometry. These remark...

There are many frameworks for modelling argumentation in logic. They include a formal representation of individual arguments and techniques for comparing conflicting arguments. A problem with these proposals is that they do not consider arguments for and against first-order formulae. We present a framework for first-order logic argumentation based on argument trees that provide a way of exhaust...

In this article we first show how the functional and the optimized functional translation from modal logic to many-sorted first-order logic can be naturally extended to the hybrid language H(@, ↓). The translation is correct not only when reasoning over the class of all models, but for any firstorder definable class. We then show that sorts can be safely removed (i.e., without affecting the sat...

We confirm a conjecture, about neat embeddings of cylindric algebras, made in 1969 by J. D. Monk, and a later conjecture by Maddux about relation algebras obtained from cylindric algebras. These results in algebraic logic have the following consequence for predicate logic: for every finite cardinal α ≥ 3 there is a logically valid sentence X, in a first-order language L with equality and exactl...

The aim of this paper is to provide a conceptual analysis of the twin paradox (TwP) within a first-order logic framework. We give a geometrical characterization of TwP and its variants, for example, one without differential aging (No-TwP). It is shown that TwP is not equivalent to the assumption of slowing down of moving clocks and No-TwP is not equivalent to the Newtonian assumption of the abs...

We present a formal first-order theory of artificial objects, i.e., objects made out of a finite number of parts and subject to assembling and dismantling processes. These processes are absolutely reversible. The theory is an extension of the theory of finite sets with urelements. The notions of transformation and identity are defined and studied on the assumption that the objects are homogeneo...