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Error-correcting codes add redundancy to transmitted data to ensure reliable communication over noisy channels. Since they form the foundations of digital communication, their correctness is a matter of concern. To enable trustful verification of linear error-correcting codes, we have been carrying out a systematic formalization in the Coq proof-assistant. This formalization includes the material that one can expect of a university class on the topic: the formalization of well-known codes (Hamming, Reed–Solomon, Bose–Chaudhuri–Hocquenghem) and also a glimpse at modern coding theory. We demonstrate the usefulness of our formalization by extracting a verified decoder for low-density parity-check codes based on the sum-product algorithm. To achieve this formalization, we needed to develop a number of libraries on top of Coq's Mathematical Components. Special care was taken to make them as reusable as possible so as to help implementers and researchers dealing with error-correcting codes in the future. [ABSTRACT FROM AUTHOR]

The article focuses on findings of a research on the use of Adaptive Toolbox theory to answer questions about how people make rational or otherwise "good" decisions in an uncertain and complex world. It states that Adaptive Toolbox theory provides an influential account with many empirical successes, and mentions that intractability is not a property that can be derived from simulations, but given a proper formalization, it can be mathematically proven. It describes phenomena like intuition.

This is the third in a three-part series of papers shortly denoted by Part I [1], and Part II [2], and Part III. The papers mentioned are devoted to some Whiteheadean theories of space and time. Part I contains a historical introduction and some facts from static mereotopology. Part II introduces a point-based definition of a dynamic model of space and a definition of a standard dynamic contact algebra based on the so-called snapshot construction. The given model has an explicit time structure with an explicit set of time points equipped with a before-after relation and a set of regions changing in time, called dynamic regions. The dynamic model of space contains several definable spatiotemporal relations between dynamic regions: space contact, time contact, precedence, and some others. In Part II, a number of statements for these relations are proven, which in the present Part III are taken as axioms for the abstract definition of some natural classes of dynamic contact algebras, considered as an algebraic formalization of dynamic mereotopology. Part III deals with a representation theory for dynamic contact algebras, and the main theorem says that each dynamic contact algebra in some natural class is representable as a standard dynamic contact algebra in the same class. [ABSTRACT FROM AUTHOR]

We outline an argument that a single-particle universe (a universe containing precisely one pointlike particle) can be described mathematically, in which observation can be considered meaningful despite the a priori impossibility of distinguishing between an observer and the observed. Moreover, we argue, such a universe can be observationally similar to the world we see around us. It is arguably impossible, therefore, to determine by experimental observation of the physical world whether the universe we inhabit contains one particle or many-modern scientific theories cannot, therefore, be regarded as descriptions of 'reality', but are at best human artefacts. Our argument uses a formal model of spacetime that can be considered either relational or substantivalist depending on one's preferred level of abstraction, and therefore suggests that this long-held distinction is also to some extent illusory. [ABSTRACT FROM AUTHOR]

The propensity interpretation of fitness (PIF) is commonly taken to be subject to a set of simple counterexamples. We argue that three of the most important of these are not counterexamples to the PIF itself, but only to the traditional mathematical model of this propensity: fitness as expected number of offspring. They fail to demonstrate that a new mathematical model of the PIF could not succeed where this older model fails. We then propose a new formalization of the PIF that avoids these (and other) counterexamples. By producing a counterexample-free model of the PIF, we call into question one of the primary motivations for adopting the statisticalist interpretation of fitness. In addition, this new model has the benefit of being more closely allied with contemporary mathematical biology than the traditional model of the PIF. 1 Introduction 1.1 The ‘Generality Problem’ 1.2 Counterexamples to the PIF 1.2.1 The moments problem 1.2.2 The delayed selection problem 1.2.3 Timing of reproduction 1.3 The need for a new model2 A New Formalization 2.1 The new model and biological theory3 Possible Objections to 3.1 Objection 1: Natural selection is short term 3.2 Objection 2: Descendants are only minimally related to ancestors 3.3 Objection 3: Evolutionary time scale is pragmatically determined 3.4 Objection 4: Long-term fitness is lineage fitness 3.5 Objection 5: The theory of evolution by natural selection fundamentally concerns trait fitness, not individual fitness4 Response to Counterexamples 4.1 Timing of reproduction 4.2 Delayed selection 4.3 The moments problem5 Conclusion [ABSTRACT FROM PUBLISHER]

In this paper we show that any reasoning process in which conclusions can be both fallible and corrigible can be formalized in terms of two approaches: (i) syntactically, with the use of defeasible reasoning, according to which reasoning consists in the construction and assessment of arguments for and against a given claim, and (ii) semantically, with the use of partial structures, which allow for the representation of less than conclusive information. We are particularly interested in the formalization of scientific reasoning, along the lines traced by Lakatos' methodology of scientific research programs. We show how current debates in cosmology could be put into this framework, shedding light on a very controversial topic. [ABSTRACT FROM AUTHOR]

It has long been a primary objective of cosmology to understand the apparent isotropy in our universe and to provide a mathematical formulation for its evolution. A promising school of thought for its explanation is quiescent cosmology, which already possesses a mathematical framework, namely the definition of an isotropic singularity, but only for the initial state of the universe. A complementary framework is necessary in order to also describe possible final states of the universe. Our new definitions of an anisotropic future endless universe and an anisotropic future singularity, whose structure and properties differ significantly from those of the isotropic singularity, offer a promising realization for this framework. The combination of the three definitions together may then provides the first complete formalization of the quiescent cosmology concept. [ABSTRACT FROM AUTHOR]

This study describes a probabilistic approach to the mathematical formalization of ideas competition in the parliamentary process as an interaction between communication and regulation. The mathematical model presented in the paper elucidates the instability of "coalition-opposition" situation and demonstrates the necessity for the imperative mandate as a reaction to opposition "irreconcilability". [ABSTRACT FROM AUTHOR]

The technological development (knowledge plus skill) of contemporary society influences its thinking already not only by means of goods and services, but also directly by shaping the public opinion and immediately by formulation of the public structure and behavior. Scale spreading of technology or purpose-oriented use of existing certain tendencies and traditions of the behavior of people suggest the idea about a possibility of the formalizations (at least on qualitative level) of the public relations and relationships. Some aspects of the analysis of the limiting contact are considered in paper on the basis of the corresponding mathematical model. [ABSTRACT FROM AUTHOR]

Out of a folklore–like fact about the counterexample function to P=NP, a function which grows about as fast as the Busy Beaver function, we review the consequences of our (with da Costa) exotic formalization for P=NP and then speculate about possible ways to extend our work. [ABSTRACT FROM PUBLISHER]

Abstract: In the literature classical conditioning is usually described and analysed informally. If formalisation is used, this is often based on mathematical models based on difference or differential equations. This paper explores a formal description and analysis of the process of trace conditioning, based on logical specification and analysis methods of dynamic properties of the process. Specific types of dynamic properties are global dynamic properties, describing properties of the process as a whole, or local dynamic properties, describing properties of basic steps in a conditioning process. If the latter type of properties are specified in an executable format, they provide a temporal declarative specification of a simulation model. By a software environment these local properties can be used to actually perform simulation. Global properties can be checked automatically for simulated or other traces. Using these methods the properties of conditioning processes informally expressed by Los and Van Den Heuvel [Los, S. A., & Van Den Heuvel, C. E. (2001). Intentional and unintentional contributions to non-specific preparation during reaction time foreperiods. Journal of Experimental Psychology: Human Perception and Performance, 27, 370–386] have been formalised and verified against a specification of local properties based on Machado’s [Machado, A. (1997). Learning the temporal dynamics of behaviour. Psychological Review, 104, 241–265] differential equation model. [Copyright &y& Elsevier]

Deals with a study which analyzed how geographic objects have been produced through data models and legitimized through academic research and discussion. Historical overview of unconsciousness; Metaphysical discussions in geographic information systems (GIS); Relationship between ontology and GIS; Discussion on formalization in GIS.

The formal concept of logical equivalence in fuzzy logic, while theoretically sound. seems impractical. The misinterpretation of this concept has led to some pessimistic conclusions Motivated by practical interpretation of truth values for fuzzy propositions, we take the class (lattice) of all subintervals of the unit interval [0. 1] as the intruth value space for fuzzy logic, subsuming the traditional class of numerical truth values from [0. 1]. The associated concept of logical equivalence is stronger than the traditional one, technically. we arc dealing with much smaller set of pairs of equivalent formulas, so that we are able to check equivalence algorithmically. The checking is done by showing that our strong equivalence notion coincides with the equivalence in logic programming. [ABSTRACT FROM AUTHOR]