We generalize Braess’s paradoxical example by defining a Braess Paradox to occur when the Wardrop equilibrium distribution of traffic flows is not strongly Pareto optimal. We characterize a Braess Paradox in terms of the solution to a mathematical program. Examples illustrate unexpected properties of these solutions. We discuss a computational approach to detecting a Braess Paradox. Keywords— M...

1 Introduction ✤ Just as there is the Russell paradox about sets, so there is the Russell-Myhill paradox of propositions. ✤ While predicativity has been well-explored as a response to the Russell paradox of sets, there seems to have been no previous attempt to set out a predicative solution to the Russell-Myhill paradox of propositions. ✤ The aim of this talk is to do that, within the framework...

To counter a general belief that all the paradoxes stem from a kind of circularity (or involve some self–reference, or use a diagonal argument) Stephen Yablo designed a paradox in 1993 that seemingly avoided self–reference. We turn Yablo’s paradox, the most challenging paradox in the recent years, into a genuine mathematical theorem in Linear Temporal Logic (LTL). Indeed, Yablo’s paradox comes ...

The biodiversity paradox is the central problem in theoretical ecology. The paradox consists in the contradiction between the competitive exclusion principle and the observed biodiversity. This contradiction is the key subject of the long-standing and continuing biodiversity debates. The paradox impedes our insights into biodiversity conservation. Previously we proved that due to a soliton-like...

% correct per task (conclusion: If A, then B) P60 P70 P90 Pvl Pac MP90 MP70 MP80 MPvl MPac Paradox 1 62.50 81.25 68.75 68.75 68.75 62.50 87.50 81.25 75.00 93.75 Paradox 2 73.33 73.33 73.33 80.00 66.67 73.33 73.33 86.67 80.00 93.33 % correct per task (conclusion: If A, then not B) Paradox 1 75.00 68.75 62.50 75.00 43.75 81.25 87.50 87.50 68.75 87.50 Paradox 2 86.67 86.67 86.67 66.67 66.67 80.00 ...

The Knowability Paradox is a logical argument showing that if all truths are knowable in principle, then all truths are, in fact, known. Many strategies have been suggested in order to avoid the paradoxical conclusion. A family of solutions – called logical revision – has been proposed to solve the paradox, revising the logic underneath, with an intuitionistic revision included. In this paper, ...

Gödel’s proof of his famous first incompleteness theorem (G1) has quite understandably long been a tantalizing target for those wanting to engineer impressively intelligent computational systems. After all, in establishing G1, Gödel did something that by any metric must be classified as stunningly intelligent. We observe that it has long been understood that there is some sort of analogical rel...

The transportation paradox is related to the classical transportation problem. For certain instances of this problem an increase in the amount of goods to be transported may lead to a decrease in the optimal total transportation cost. Thus this phenomenon has also been named the more-for-less-paradox. Even though the paradox has been known since the early days of linear programming, it has got ...

Asthma is a heterogeneous disease, in which asthmatic patients present with different clinical phenotypes, variable endotypes, and different response to asthma medicines. Thus, we are faced with an asthma paradox; asthma is diagnosed subjectively by clinical history and treated with biologically active drugs. To solve this paradox, we need objective airway biomarkers to tailor the proper medica...

The Knowability Paradox is a logical argument which states that if all truths are knowable, then all truths are actually known. In 1963 Frederich Fitch published ‘A Logical Analysis of Some Value Concepts’[3]. This brief article appeared on the Journal of Symbolic Logic and it immediately became a classic of philosophical logic. It is in this paper that Fitch presented the Knowability Paradox, ...