Related papers: Is 1+1=2 an empirical proposition?
We study density of rational languages under shift invariant probability measures on spaces of two-sided infinite words, which generalizes the classical notion of density studied in formal languages and automata theory. The density for a…
A probabilistic propositional logic, endowed with an epistemic component for asserting (non-)compatibility of diagonizable and bounded observables, is presented and illustrated for reasoning about the random results of projective…
A theory of how agents can come to understand a language is presented. If understanding a sentence $\alpha$ is to associate an operator with $\alpha$ that transforms the representational state of the agent as intended by the sender, then…
We propose a new definition of actual cause, using structural equations to model counterfactuals. We show that the definition yields a plausible and elegant account of causation that handles well examples which have caused problems for…
Associating a physical process with the pure entangled state 1/sqrt 2 (|00> + |11>) is an idealization unless the pair is so prepared using an appropriate quantum gate operating on a known state. Questions related to the reference frame for…
We axiomatize the first-order theories of exponential integer parts of real-closed exponential fields in a language with $2^x$, in a language with a predicate for powers of 2, and in the basic language of ordered rings. In particular, the…
In this paper we examine different meaning representations that are commonly used in different natural language applications today and discuss their limits, both in terms of the aspects of the natural language meaning they are modelling and…
Analogy has received attention as a form of inductive reasoning in the empirical sciences. However, its role in pure mathematics has received less consideration. This paper provides an account of how an analogy with a more familiar…
This talk is a sneak preview of the project, 'proof theory for theories of ordinals'. Background, aims, survey and furture works on the project are given. Subsystems of second order arithmetic are embedded in recursively large ordinals and…
This paper proposes an alternative language for expressing results of the algorithmic theory of randomness. The language is more precise in that it does not involve unspecified additive or multiplicative constants, making mathematical…
A definition of a {\it Realistic} Physics Theory is proposed based on the idea that, at all time, the set of physical properties possessed (at that time) by a system should unequivocally determine the probabilities of outcomes of all…
We consider team semantics for propositional logic, continuing our previous work (Yang & V\"a\"an\"anen 2016). In team semantics the truth of a propositional formula is considered in a set of valuations, called a team, rather than in an…
As interaction between autonomous agents, communication can be analyzed in game-theoretic terms. Meaning game is proposed to formalize the core of intended communication in which the sender sends a message and the receiver attempts to infer…
Representing the semantics of linguistic items in a machine-interpretable form has been a major goal of Natural Language Processing since its earliest days. Among the range of different linguistic items, words have attracted the most…
In this note we suggest that difficulties encountered in natural language semantics are, for the most part, due to the use of mere symbol manipulation systems that are devoid of any content. In such systems, where there is hardly any link…
Most physics theories are deterministic, with the notable exception of quantum mechanics which, however, comes plagued by the so-called measurement problem. This state of affairs might well be due to the inability of standard mathematics to…
Cognitive theories for reasoning are about understanding how humans come to conclusions from a set of premises. Starting from hypothetical thoughts, we are interested which are the implications behind basic everyday language and how do we…
Counterfactual reasoning and contextuality is defined and critically evaluated with regard to its nonempirical content. To this end, a uniqueness property of states, explosion views and link observables are introduced. If only a single…
This paper proposes a definition of what it means for one system description language to encode another one, thereby enabling an ordering of system description languages with respect to expressive power. I compare the proposed definition…
(from the talk:) I shall here speak on gravity in (1+1)-dimensional space-time --- lineal gravity. The purpose of studying lower dimensional theories, and specifically lower dimensional gravity, is to gain insight into difficult…