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Handbook of Grammatical Evolution pp 189–218Cite as

GE and Semantics

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Abstract

The main goal of this chapter is to explain in a comprehensible way the semantic context in formal language theory. This is necessary to properly understand the attempts to extend Grammatical Evolution (GE) to include semantics. Several approaches from different researchers to handle semantics, both directly and indirectly, will be briefly introduced. Finally, previous works by the authors will be described in depth.

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Notes

  1. 1.

    Let’s consider f as f: [0, |w|] → [−|w|, |w|] so that f(i) = ♯ a(w[0, i]) − ♯ b(|w[0, i]) and where w[0, i] is the subsequence of w respectively starting and ending in 0 and i. It is clear that |f(i + 1) − f(i)| = 1∀i. For this step of the proof, it is easy to consider either a version of Bonzano’s theorem for this kind of functions; or to define a function to which Bolzano’s result could be applied. In the first case, notice that for every zero of f (∀i|f(i) = 0); the sequence of points {(i, −1), (i, 0), (i, 1)} (or {(i, 1), (i, 0), (i, −1)}) always belongs to f. In the last case, one could consider the continuous function f′ that can be drawn connecting consecutive points of f or even a polynomial interpolation that preserves its points (all of them or at least the most relevant, around its zeros).

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Acknowledgements

This work has been supported by several research grants: Spanish Ministry of Science and Education under Project Code TIN2014-56494-C4-4-P (ephemeCH) and TIN2017-85727-C4-3-P (DeepBio). We thank also Manuel Alfonseca’s help to improve this work.

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Authors and Affiliations

  1. UAM, Computer Engineering Department, Madrid, Spain

    Marina de la Cruz Echeandía, Younis R. SH. Elhaddad, Suzan Awinat & Alfonso Ortega

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  1. Marina de la Cruz Echeandía
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  4. Alfonso Ortega
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Correspondence to Alfonso Ortega .

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  1. Department of Computer Science and Information Systems, University of Limerick, Castletroy, Limerick, Ireland

    Conor Ryan

  2. School of Business, University College Dublin, Dublin, Ireland

    Michael O'Neill

  3. Department of Computer Science and Information Systems, University of Limerick, Castletroy, Limerick, Ireland

    JJ Collins

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de la Cruz Echeandía, M., Elhaddad, Y.R.S., Awinat, S., Ortega, A. (2018). GE and Semantics. In: Ryan, C., O'Neill, M., Collins, J. (eds) Handbook of Grammatical Evolution. Springer, Cham. https://doi.org/10.1007/978-3-319-78717-6_8

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  • DOI: https://doi.org/10.1007/978-3-319-78717-6_8

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