Mathematics and philosophy have historically enjoyed a mutually beneficial and productive relationship, as a brief review of the work of mathematician-philosophers such as Descartes, Leibniz, Bolzano, Dedekind, Frege, Brouwer, Hilbert, Gödel, and Weyl easily confirms. In the last century, it was especially mathematical logic and research in the foundations of mathematics which, to a significant...

(vastly abbreviated and horribly simpliied) Michaa l Walicki 1997 The term \logic" may be, very roughly and vaguely, associated with something like \correct thinking". Aristotle deened a syllogism as \discourse in which, certain things being stated something other than what is stated follows of necessity from their being so." And, in fact, this intuition not only lies at its origin, ca. 500 BC,...

The aim of this paper is not to provide any systematic reconstruction of Kreisel’s views but only to discuss some claims concerning the relationship between mathematical logic and the philosophy of mathematics that repeatedly occur in his writings. Although I do not know to what extent they are representative of his present position, they correspond to widespread views of the logical community ...

in this paper, a control strategy is proposed for control of ankle movement on animals using intraspinal microstimulation (isms). the proposed method is based on fuzzy logic control. fuzzy logic control is a methodology of intelligent control that mimics human decision-making process. this type of control method can be very useful for the complex uncertain systems that their mathematical model ...

Given the importance of recursion in modern linguistics, there ought to be much to commend in Watumull et al.’s (2014) attempt to clarify what recursion is (or ought to be); I have trudged this very terrain myself, using some of the same sources, and in order to make similar points (e.g., Lobina, 2011, but especially in Lobina, 2012). However, there are so many issues with Watumull et al.’s own...

In this paper, first-order logic is interpreted in the framework of universal algebra, using the clone theory developed in three previous papers [1] [2] and [3]. We first define the free clone T pL, Cq of terms of a first order language L over a set C of parameters in a standard way. The free right algebra FpL, Cq of formulas over the clone T pL, Cq of terms is then generated by atomic formulas...

These notes were written by Wang Yafeng following a course of three intensive lectures on classical themes in mathematical modal logic given by Johan van Benthem in the Berkeley-Stanford Logic Circle, San Francisco, May 2015. Some of this material was collected in the monograph van Benthem [13], [16], other parts come from later publications. We will provide some references to further relevant ...

The article retraces major events and milestones in the mutual influences between mathematical logic and computer science since the 1950s.

Modern mathematical logic is a multifaceted subject, which concerns itself with the strengths and limitations of formal proofs and algorithms and the relationship between language and mathematical structure. Modern mathematical logic also addresses foundational issues that arise in mathematics. This commentary summarizes the groundbreaking results of Malliaris and Shelah (1), recently published...

The paper proposes and studies temporal logics for attributed words, that is, data words with a (finite) set of (attribute,value)-pairs at each position. It considers a basic logic which is a semantical fragment of the logic LTL1 of Demri and Lazic with operators for navigation into the future and the past. By reduction to the emptiness problem for data automata it is shown that this basic logi...