119 research outputs found
Studying Algebraic Structures Using Prover9 and Mace4
In this chapter we present a case study, drawn from our research work, on the
application of a fully automated theorem prover together with an automatic
counter-example generator in the investigation of a class of algebraic
structures. We will see that these tools, when combined with human insight and
traditional algebraic methods, help us to explore the problem space quickly and
effectively. The counter-example generator rapidly rules out many false
conjectures, while the theorem prover is often much more efficient than a human
being at verifying algebraic identities. The specific tools in our case study
are Prover9 and Mace4; the algebraic structures are generalisations of Heyting
algebras known as hoops. We will see how this approach helped us to discover
new theorems and to find new or improved proofs of known results. We also make
some suggestions for how one might deploy these tools to supplement a more
conventional approach to teaching algebra.Comment: 21 pages, to appear as Chapter 5 in "Proof Technology in Mathematics
Research and Teaching", Mathematics Education in the Digital Era 14, edited
by G. Hanna et al. (eds.), published by Springe
Logics for the Relational Syllogistic
The Aristotelian syllogistic cannot account for the validity of many
inferences involving relational facts. In this paper, we investigate the
prospects for providing a relational syllogistic. We identify several fragments
based on (a) whether negation is permitted on all nouns, including those in the
subject of a sentence; and (b) whether the subject noun phrase may contain a
relative clause. The logics we present are extensions of the classical
syllogistic, and we pay special attention to the question of whether reductio
ad absurdum is needed. Thus our main goal is to derive results on the existence
(or non-existence) of syllogistic proof systems for relational fragments. We
also determine the computational complexity of all our fragments
Evidence for the Gompertz Curve in the Income Distribution of Brazil 1978-2005
This work presents an empirical study of the evolution of the personal income
distribution in Brazil. Yearly samples available from 1978 to 2005 were studied
and evidence was found that the complementary cumulative distribution of
personal income for 99% of the economically less favorable population is well
represented by a Gompertz curve of the form , where
is the normalized individual income. The complementary cumulative
distribution of the remaining 1% richest part of the population is well
represented by a Pareto power law distribution . This
result means that similarly to other countries, Brazil's income distribution is
characterized by a well defined two class system. The parameters , ,
, were determined by a mixture of boundary conditions,
normalization and fitting methods for every year in the time span of this
study. Since the Gompertz curve is characteristic of growth models, its
presence here suggests that these patterns in income distribution could be a
consequence of the growth dynamics of the underlying economic system. In
addition, we found out that the percentage share of both the Gompertzian and
Paretian components relative to the total income shows an approximate cycling
pattern with periods of about 4 years and whose maximum and minimum peaks in
each component alternate at about every 2 years. This finding suggests that the
growth dynamics of Brazil's economic system might possibly follow a
Goodwin-type class model dynamics based on the application of the
Lotka-Volterra equation to economic growth and cycle.Comment: 22 pages, 15 figures, 4 tables. LaTeX. Accepted for publication in
"The European Physical Journal B
A system of relational syllogistic incorporating full Boolean reasoning
We present a system of relational syllogistic, based on classical
propositional logic, having primitives of the following form:
Some A are R-related to some B;
Some A are R-related to all B;
All A are R-related to some B;
All A are R-related to all B.
Such primitives formalize sentences from natural language like `All students
read some textbooks'. Here A and B denote arbitrary sets (of objects), and R
denotes an arbitrary binary relation between objects. The language of the logic
contains only variables denoting sets, determining the class of set terms, and
variables denoting binary relations between objects, determining the class of
relational terms. Both classes of terms are closed under the standard Boolean
operations. The set of relational terms is also closed under taking the
converse of a relation. The results of the paper are the completeness theorem
with respect to the intended semantics and the computational complexity of the
satisfiability problem.Comment: Available at
http://link.springer.com/article/10.1007/s10849-012-9165-
Zinc oxide for electronic, photovoltaic and optoelectronic applications
We demonstrate that the atomic layer deposition (ALD) technique has large potential to be widely used in a production of ZnO films for applications in electronic, photovoltaic (PV) and optoelectronic devices. Low growth temperature makes the ALD-grown ZnO films suitable for construction of various semiconductor/organic material hybrid structures. This opens possibilities of construction of novel devices based on very cheap organic materials. This includes organic light emitting diodes and PV cells of the third generation, as discussed in the present work
Antimicrobial lubricant formulations containing poly(hydroxybenzene)-trimethoprim conjugates synthesized by tyrosinase
Poly(hydroxybenzene)-trimethoprim conjugates were prepared using methylparaben as substrate of the oxida- tive enzyme tyrosinase. MALDI-TOF MS analysis showed that the enzymatic oxidation of methylparaben alone leads to the poly(hydroxybenzene) formation. In the presence of tri- methoprim, the methylparaben tyrosinase oxidation leads poly(hydroxybenzene)-trimethoprim conjugates. All of these compounds were incorporated into lubricant hydroxyethyl cellulose/glycerol mixtures. Poly(hydroxybenzene)-trimetho- prim conjugates were the most effective phenolic structures against the bacterial growth reducing by 96 and 97 % of Escherichia coli and Staphylococcus epidermidis suspen- sions, respectively (after 24 h). A novel enzymatic strategy to produce antimicrobial poly(hydroxybenzene)-antibiotic conjugates is proposed here for a wide range of applications on the biomedical field.The authors Idalina Gonçalves and Cláudia
Botelho would like to acknowledge the NOVO project (FP7-HEALTH-
2011.2.3.1- 5) for funding. Loïc Hilliou acknowledges the financial support
by FCT – Foundation for Science and Technology, Portugal
(501100001871), through Grant PEst-C/CTM/LA0025/2013 - Strategic
Project - LA 25 - 2013–2014, and by Programa Operacional Regional
do Norte (ON.2) through the project BMatepro – Optimizing Materials
and Processes^, with reference NORTE-07-0124-FEDER-000037
FEDER COMPETE
aristotle's demonstrative logic
Demonstrative logic, the study of demonstration as opposed to persuasion, is the subject of Aristotle's two-volume Analytics. Many examples are geometrical. Demonstration produces knowledge (of the truth of propositions). Persuasion merely produces opinion. Aristotle presented a general truth-and-consequence conception of demonstration meant to apply to all demonstrations. According to him, a demonstration, which normally proves a conclusion not previously known to be true, is an extended argumentation beginning with premises known to be truths and containing a chain of reasoning showing by deductively evident steps that its conclusion is a consequence of its premises. In particular, a demonstration is a deduction whose premises are known to be true. Aristotle's general theory of demonstration required a prior general theory of deduction presented in the Prior Analytics. His general immediate-deduction-chaining conception of deduction was meant to apply to all deductions. According to him, any deduction that is not immediately evident is an extended argumentation that involves a chaining of intermediate immediately evident steps that shows its final conclusion to follow logically from its premises. To illustrate his general theory of deduction, he presented an ingeniously simple and mathematically precise special case traditionally known as the categorical syllogisti
A method for finding new sets of axioms for classes of semigroups
We introduce a general technique for finding sets of axioms for a given class of semigroups. To illustrate the technique, we provide new sets of defining axioms for groups of exponent n, bands, and semilattices
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