If logic is the general study of a priori valid reasoning, then where is the paradigmatic area where we see this reasoning in its full glory? To some, this is clearly mathematics, where precision is relentless, and strings of inferences are taken to impressive lengths. But on another view, the highest form of reasoning is displayed in the ordinary world of common sense – say, when engaging in c...

A framework is developed that extends Hilbert-style proof systems for propositional and modal logics to comprehend their team-based counterparts. The method is applied to classical propositional logic and the modal logic K. Complete axiomatizations for their team-based extensions, propositional team logic PTL and modal team logic MTL, are presented. 1998 ACM Subject Classification F.4.1 Mathema...

1. INTRODUCTION AND EARLY DEVELOPMENTS. Logic and foundations are a domain of mathematics concerned with basic mathematical structures (in terms of which one can define all other mathematical structures), with the correctness and significance of mathematical reasoning, and with the effectiveness of mathematical computations. In the twentieth century, these areas have crystallized into three lar...

When we compare mathematics with logic in regard to the role assigned to these two domains of knowledge within philosophical thinking, we find a disagreement among philosophers. For some logic is singled out; for them, logic in the broader sense is the λóγoς, that what is rational, and logic in the narrower sense is the inventory of elementary insights which should lie beneath all consideration...

Location The meeting takes place on De Uithof in Utrecht.

However, the implication from (1) to (2) is equivalent to the principle of dependent choices (as the reader can show for himself) and cannot be proved in ZF. A relation < on X is called well-founded if any of these statements holds. Intuitionistically, the three statements are far from equivalent (hence, in formalizing an intuitionistic notion of well-foundedness, care is needed). Notion (1) is...

As a higher cognitive function in humans, mathematics is supported by parietal and prefrontal brain regions. Here, we give an integrative account of the role of the different brain systems in processing the semantics of mathematical logic from the perspective of macroscopic polysynaptic networks. By comparing algebraic and arithmetic expressions of identical underlying structure, we show how th...

We advocates here the use of (mathematical) logic for systems biology, as a unified framework well suited for both modeling the dynamic behaviour of biological systems, expressing properties of them, and verifying these properties. The potential candidate logics should have a traditional proof theoretic pedigree (including a sequent calculus presentation enjoying cut-elimination and focusing), ...