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Proto-Indo-European Lexicon (PIE Lexicon)
Proto-Indo-European Lexicon (PIE Lexicon) is the generative etymological dictionary of Indo-European languages. PIE Lexicon is an academic open source database published online at the address http://pielexicon.hum.helsinki.fi.

PIE Lexicon is an etymological dictionary that will comprise the main bulk of the vocabulary of more than hundred most ancient Indo-European languages when the first phase of the project has been accomplished. When ready the project will expand to its second phase in which the later Indo-European languages will be added to the database.

The next-generation feature of the dictionary is the automatic generation of the Indo-European data, quoted in a stem form (i.e. without inflectional endings), on the basis of the digitised Indo-European sound laws and a primary phoneme inventory postulated for the Proto-Indo-European languages.

System PIE: The Primary Phoneme Inventory and the Sound Law System for Proto-Indo-European
The background of Proto-Indo-European Lexicon is Jouna Pyysalo‘s dissertation (2013). System PIE: The Primary Phoneme Inventory and Sound Law System for Proto-Indo-European. In this monography Pyysalo, presents the solution of the Proto-Indo-European laryngeal problem and the primary phoneme inventory for Proto-Indo-European. In the chapters dealing with functionally defined classes of phonemes he throughly revises, corrects and finally complets the Indo-European sound laws into a system consistent mutually and with the data.

Comparative Method of Reconstruction in Indo-European linguistics
Pyysalo's work is committed to the method of natural science, a suitable choice as the Comparative Method of reconstruction in Indo-European linguistics is presented as a branch of natural science within humanities.

The solution of the Proto-Indo-European laryngeal problem
The solution of the Proto-Indo-European laryngeal problem, viz. the question of the phonetic interpretation and the number of "laryngeals" of the proto-language has been disputed ever since Bedřich Hrozný's proof of the Indo-European character of the Hittite language. In Pyysalo 2013 an inductive solution to the problem is presented according to which 1. Proto-Indo-European had a single "laryngeal", actually a glottal fricative with voiceless and voiced variants PIE *h and PIE *ɦ, both segmentally preserved in Hitt. ḫ. 2. Proto-Indo-European *h/ɦ was always accompanied with PIE *ɑ (the reinterpreted Schwa Indogermanicum) thus appearing in diphonemic pairs PIE *hɑ *ɑh *ɦɑ *ɑɦ In the cover symbol notation used in the laryngeal theory (LT) this equals to the system of items LT *h2 *2h *ɦ2 *2ɦ (with LT *2 = PIE *ɑ).

The Primary Phoneme Inventory of Proto-Indo-European
The significance of the solution of the PIE laryngeal problem lies in the fact that the "laryngeal" is the last uninterpreted piece of the PIE phoneme inventory. With the missing link of the PIE sound system at his disposal Pyysalo segmentally analyses the traditionally postulated proto-phonemes of the historical theories and comparatively infers a minimal set of phonemes for the PIE consisting of fourteen phonemes with two realisations for each: PIE *o/ō *e/ē *ɑ/ɑ̄? *h/ɦ *i/i̯ *k/g *l/l̥ *m/m̥ *n/n̥ *p/b *r/r̥ *s/z *t/d *u/u̯

Operating System PIE Lexicon (OS PIE Lexicon)
The digitalisation of Pyysalo 2013 has been ongoing since June 2014 in the PIE Lexicon address http://pielexicon.hum.helsinki.fi with a straightforward goal of implementation of the data and the sound laws into a platform using finite state technology (Foma application), thus effectively upgrading the earlier System PIE into a Operating System (OS) PIE Lexicon, the next-generation etymological dictionary of Indo-European languages.

The key difference of between PIE Lexicon and all its predecessors (including Pokorny and LIV2, etc.) is not as much the digital platform but the digitalised, chronologically arranged sound law (or Foma-)scripts written for each language presented in PIE Lexicon. By means of the Foma-scripts the OS PIE Lexicon automatically (re-)generates the Indo-European words exactly as they were once born from Proto-Indo-European.

General significance of the PIE Lexicon for Indo-European linguistics
One can readily compare the process to Newton's introduction of the laws of gravity and the calculus for the complex computations required in order to predict the movements of the planets and other objects: Instead of only quoting the Indo-European forms PIE Lexicon predicts that there is such-and-such word in a such-and-such language.

As such the Comparative Method of reconstruction in Indo-European linguistics is in a transition to become a branch of natural science.

Historical Background of (OS) PIE Lexicon
Historically PIE Lexicon continues the comparative tradition of Indo-European linguistics, which is often contrasted to the Laryngeal Theory, attempting to offer a more regular account of PIE ablaut https://en.wikipedia.org/wiki/Laryngeal_theory.

Despite this a straightforward opposition of the two views is, however, less recommendable: Rather than standing in opposition to the Laryngeal theory the System PIE (and OS PIE Lexicon) can be characterised as containing elements from all historical mainstream schools of thought, i.e. from the Paleogrammarians, the Neogrammarians, the Laryngeal Theory and the monolaryngealism.

Thus, for instance, the solution of the laryngeal problem, PIE *hɑ *ɑh *ɦɑ *ɑɦ, contains PIE *ɑ, the former Schwa Indogermanicum inherited from the Neogrammarians, the single laryngeal from the monolaryngealism, but also accepts the colouring rules of the laryngeal theory, thus e.g. deriving the vowel Neogr. *a from PIE *ɑe (cf. Møller's Ae -> a) and so forth.

Problems and criticism
Hitherto the main problem (and criticism) of the theory is the lack of typological parallel for the existence of diphonemic PIE *hɑ *ɑh *ɦɑ *ɑɦ in the languages of the world, as already mentioned in Pyysalo (2013: 461-2): Although already the Neogrammarians proved the existence of the vowel *ǝ (reinterpreted as PIE *ɑ in System PIE) and the Anatolian data preserves a single laryngeal Hitt. ḫ, "It is desirable that a typological parallel be found for a system of phonemes PIE *ɑ and PIE *ḫ choosing each other (strict phonotactical selection) in diphonemic PIE *ɑḫ : ḫɑ (...)”