Inductive Reasoning Games as Influenza Vaccination Models: Mean Field Analysis

We define and analyze an inductive reasoning game of voluntary yearly vaccination in order to establish whether or not a population of individuals acting in their own self-interest would be able to prevent influenza epidemics. We find that epidemics are rarely prevented. We also find that severe epidemics may occur without the introduction of pandemic strains. We further address the situation where market incentives are introduced to help ameliorating epidemics. Surprisingly, we find that vaccinating families exacerbates epidemics. However, a public health program requesting prepayment of vaccinations may significantly ameliorate influenza epidemics.Comment: 20 pages, 7 figure

Factors and processes in children's transitive deductions

Transitive tasks are important for understanding how children develop socio-cognitively. However, developmental research has been restricted largely to questions surrounding maturation. We asked 6-, 7- and 8-year-olds (N = 117) to solve a composite of five different transitive tasks. Tasks included conditions asking about item-C (associated with the marked relation) in addition to the usual case of asking only about item-A (associated with the unmarked relation). Here, children found resolving item-C much easier than resolving item-A, a finding running counter to long-standing assumptions about transitive reasoning. Considering gender perhaps for the first time, boys exhibited higher transitive scores than girls overall. Finally, analysing in the context of one recent and well-specified theory of spatial transitive reasoning, we generated the prediction that reporting the full series should be easier than deducing any one item from that series. This prediction was not upheld. We discuss amendments necessary to accommodate all our earlier findings

Getting one step closer to deduction: Introducing an alternative paradigm for transitive inference

This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ 2008 Psychology Press.Transitive inference is claimed to be “deductive”. Yet every group/species ever reported apparently uses it. We asked 58 adults to solve five-term transitive tasks, requiring neither training nor premise learning. A computer-based procedure ensured all premises were continually visible. Response accuracy and RT (non-discriminative nRT) were measured as is typically done. We also measured RT confined to correct responses (cRT). Overall, very few typical transitive phenomena emerged. The symbolic distance effect never extended to premise recall and was not at all evident for nRT; suggesting the use of non-deductive end-anchor strategies. For overall performance, and particularly the critical B?D inference, our findings indicate that deductive transitive inference is far more intellectually challenging than previously thought. Contrasts of our present findings against previous findings suggest at least two distinct transitive inference modes, with most research and most computational models to date targeting an associative mode rather than their desired deductive mode. This conclusion fits well with the growing number of theories embracing a “dual process” conception of reasoning. Finally, our differing findings for nRT versus cRT suggest that researchers should give closer consideration to matching the RT measure they use to the particular conception of transitive inference they pre-held

Tableaux Modulo Theories Using Superdeduction

We propose a method that allows us to develop tableaux modulo theories using the principles of superdeduction, among which the theory is used to enrich the deduction system with new deduction rules. This method is presented in the framework of the Zenon automated theorem prover, and is applied to the set theory of the B method. This allows us to provide another prover to Atelier B, which can be used to verify B proof rules in particular. We also propose some benchmarks, in which this prover is able to automatically verify a part of the rules coming from the database maintained by Siemens IC-MOL. Finally, we describe another extension of Zenon with superdeduction, which is able to deal with any first order theory, and provide a benchmark coming from the TPTP library, which contains a large set of first order problems.Comment: arXiv admin note: substantial text overlap with arXiv:1501.0117

The "Artificial Mathematician" Objection: Exploring the (Im)possibility of Automating Mathematical Understanding

Reuben Hersh confided to us that, about forty years ago, the late Paul Cohen predicted to him that at some unspecified point in the future, mathematicians would be replaced by computers. Rather than focus on computers replacing mathematicians, however, our aim is to consider the (im)possibility of human mathematicians being joined by “artificial mathematicians” in the proving practice—not just as a method of inquiry but as a fellow inquirer

A comparison of techniques for learning and using mathematics and a study of their relationship to logical principles

Various techniques exist for learning mathematical concepts, like experimentation and exploration, respectively using mathematics, like modelling and simulation. For a clear application of such techniques in mathematics education, there should be a clear distinction between these techniques. A recently developed theory of fuzzy concepts can be applied to analyse the four mentioned concepts. For all four techniques one can pose the question of their relationship to deduction, induction and abduction as logical principles. An empirical study was conducted with 12-13 aged students, aiming at checking the three reasoning processes

The AutoProof Verifier: Usability by Non-Experts and on Standard Code

Formal verification tools are often developed by experts for experts; as a result, their usability by programmers with little formal methods experience may be severely limited. In this paper, we discuss this general phenomenon with reference to AutoProof: a tool that can verify the full functional correctness of object-oriented software. In particular, we present our experiences of using AutoProof in two contrasting contexts representative of non-expert usage. First, we discuss its usability by students in a graduate course on software verification, who were tasked with verifying implementations of various sorting algorithms. Second, we evaluate its usability in verifying code developed for programming assignments of an undergraduate course. The first scenario represents usability by serious non-experts; the second represents usability on "standard code", developed without full functional verification in mind. We report our experiences and lessons learnt, from which we derive some general suggestions for furthering the development of verification tools with respect to improving their usability.Comment: In Proceedings F-IDE 2015, arXiv:1508.0338