Related papers: Logical foundations: Personal perspective
Particularly in transgender and nonbinary (TGNB) communities, it is an increasingly common practice to publicly share one's personal pronouns so that we may be gendered correctly in others' speech. Many of us have nuanced desires for how we…
In this article we determine the implicational fragments of most of the known subintuitionistic logics.
Computability logic is a formal theory of (interactive) computability in the same sense as classical logic is a formal theory of truth. This approach was initiated very recently in "Introduction to computability logic" (Annals of Pure and…
In this article we present and describe a notion of "logical perfection". We extract the notion of "perfection" from the contemporary logical concept of categoricity. Categoricity (in power) has become in the past half century a main driver…
A popular scientific contribution should not contradict any established facts and ought to be understandable. I complied with both these requirements and am offering a sufficiently full introduction to probability theory. Furthermore, I…
We present a rational analysis of curiosity, proposing that people's curiosity is driven by seeking stimuli that maximize their ability to make appropriate responses in the future. This perspective offers a way to unify previous theories of…
This paper from 2008 is the first in a series of three related papers on modal methods in interpretability logics and applications. In this first paper the foundations are laid for later results. These foundations consist of a thorough…
This is a broad and in places unconventional overview of the strengths and shortcomings of our standard models of fundamental physics and of cosmology. The emphasis is on ideas that have accessible experimental consequences. It becomes…
Contemporary semantic description of logic is based on the ontology of all possible interpretations, an insufficiently clear metaphysical concept. In this article, logic is described as the internal organization of language. Logical…
Possibilistic logic, an extension of first-order logic, deals with uncertainty that can be estimated in terms of possibility and necessity measures. Syntactically, this means that a first-order formula is equipped with a possibility degree…
A model of knowledge representation is described in which propositional facts and the relationships among them can be supported by other facts. The set of knowledge which can be supported is called the set of cognitive units, each having…
In this paper I consider some logical and mathematical aspects of the discussion of the identity and individuality of quantum entities. I shall point out that for some aspects of the discussion, the logical basis cannot be put aside; on the…
Traditional cognitive science rests on a foundation of classical logic and probability theory. This foundation has been seriously challenged by several findings in experimental psychology on human decision making. Meanwhile, the formalism…
Personal view of author on goals and content of Mathematical Physics.
We provide an overview of the results we have attained in the last decade on the identification of quantum structures in cognition and, more specifically, in the formalization and representation of natural concepts. We firstly discuss the…
Logical formalisms provide a natural and concise means for specifying and reasoning about preferences. In this paper, we propose lexicographic logic, an extension of classical propositional logic that can express a variety of preferences,…
Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as…
This is not in any way meant to be a complete survey on positive curvature. Rather it is a short essay on the fascinating changes in the landscape surrounding positive curvature. In particular, details and many results and references are…
We survay some nice result concerning the irrationals with a metric space point of view.Here is ofcourse nothing new may be or an expert in this field.
These informal notes discuss a few basic notions and examples, with emphasis on constructions that may be relevant for analysis on metric spaces.