E-Generalization Using Grammars

We extend the notion of anti-unification to cover equational theories and present a method based on regular tree grammars to compute a finite representation of E-generalization sets. We present a framework to combine Inductive Logic Programming and E-generalization that includes an extension of Plotkin's lgg theorem to the equational case. We demonstrate the potential power of E-generalization by three example applications: computation of suggestions for auxiliary lemmas in equational inductive proofs, computation of construction laws for given term sequences, and learning of screen editor command sequences.Comment: 49 pages, 16 figures, author address given in header is meanwhile outdated, full version of an article in the "Artificial Intelligence Journal", appeared as technical report in 2003. An open-source C implementation and some examples are found at the Ancillary file

Complex systems and the history of the English language

Complexity theory (Mitchell 2009, Kretzschmar 2009) is something that historical linguists not only can use but should use in order to improve the relationship between the speech we observe in historical settings and the generalizations we make from it. Complex systems, as described in physics, ecology, and many other sciences, are made up of massive numbers of components interacting with one another, and this results in self-organization and emergent order. For speech, the “components” of a complex system are all of the possible variant realizations of linguistic features as they are deployed by human agents, speakers and writers. The order that emerges in speech is simply the fact that our use of words and other linguistic features is significantly clustered in the spatial and social and textual groups in which we actually communicate. Order emerges from such systems by means of self-organization, but the order that arises from speech is not the same as what linguists study under the rubric of linguistic structure. In both texts and regional/social groups, the frequency distribution of features occurs as the same pattern: an asymptotic hyperbolic curve (or “A-curve”). Formal linguistic systems, grammars, are thus not the direct result of the complex system, and historical linguists must use complexity to mediate between the language production observed in the community and the grammars we describe. The history of the English language does not proceed as regularly as like clockwork, and an understanding of complex systems helps us to see why and how, and suggests what we can do about it. First, the scaling property of complex systems tells us that there are no representative speakers, and so our observation of any small group of speakers is unlikely to represent any group at a larger scale—and limited evidence is the necessary condition of many of our historical studies. The fact that underlying complex distributions follow the 80/20 rule, i.e. 80% of the word tokens in a data set will be instances of only 20% of the word types, while the other 80% of the word types will amount to only 20% of the tokens, gives us an effective tool for estimating the status of historical states of the language. Such a frequency-based technique is opposed to the typological “fit” technique that relies on a few texts that can be reliably located in space, and which may not account for the crosscutting effects of text type, another dimension in which the 80/20 rule applies. Besides issues of sampling, the frequency-based approach also affects how we can think about change. The A-curve immediately translates to the S-curve now used to describe linguistic change, and explains that “change” cannot reasonably be considered to be a qualitative shift. Instead, we can use to model of “punctuated equilibrium” from evolutionary biology (e.g., see Gould and Eldredge 1993), which suggests that multiple changes occur simultaneously and compete rather than the older idea of “phyletic gradualism” in evolution that corresponds to the traditional method of historical linguistics. The Great Vowel Shift, for example, is a useful overall generalization, but complex systems and punctuated equilibrium explain why we should not expect it ever to be “complete” or to appear in the same form in different places. These applications of complexity can help us to understand and interpret our existing studies better, and suggest how new studies in the history of the English language can be made more valid and reliable

Mild context-sensitivity and tuple-based generalizations of context-free grammar

This paper classifies a family of grammar formalisms that extend context-free grammar by talking about tuples of terminal strings, rather than independently combining single terminal words into larger single phrases. These include a number of well-known formalisms, such as head grammar and linear context-free rewriting systems, but also a new formalism, (simple) literal movement grammar, which strictly extends the previously known formalisms, while preserving polynomial time recognizability. The descriptive capacity of simple literal movement grammars is illustrated both formally through a weak generative capacity argument and in a more practical sense by the description of conjunctive cross-serial relative clauses in Dutch. After sketching a complexity result and drawing a number of conclusions from the illustrations, it is then suggested that the notion of mild context-sensitivity currently in use, that depends on the rather loosely defined concept of constant growth, needs a modification to apply sensibly to the illustrated facts; an attempt at such a revision is proposed

A Simple Uniform Semantics for Concatenation-based Grammar

We define a more formal version of literal movement grammar (LMG) as outlined in [Gro95c], in such a way that it provides a simple framework that incorporates a large family of grammar formalisms (Head Grammar [Pol84], LCFRS, [Wei88]), PMCFG, [KNSK92] and String Attributed Grammars [Eng86]). The semantics is (both in rewriting and least fixed point definitions) simple and elegant, and sheds some new light on shared properties of the mentioned formalisms. We then define a restricted version called simple LMG and show that it generates languages that are not mildly context sensitive, yet preserves the polynomial time recognition property of LCFRS

The comprehension revolution : a twenty-year history of process and practice related to reading comprehension

Includes bibliographie

Toward a Cognitive Classical Linguistics. The Embodied Basis of Constructions in Greek and Latin

The volume that gathers a series of papers bringing together the study of grammatical and syntactic constructions in Greek and Latin under the perspective of theories of embodied meaning developed in cognitive linguistics

Grammar of Location and Motion in Zande

In Zande expressions of position and motion are arranged on a gamut in correlation with increasing syntactic complexity. Topological relations, expressed by basic locative construction are at the left end, directed motion at the right end. Directed translational motion is marked by the preposition ku, which also marks angular location. Topological relations, in situ motion and undirected translational motion do not get a specific marking. This indicates the interrelatedness of stasis and motion on the one hand and undirected and directed motion on the other hand

Providence, Temporal Authority, and the Illustrious Vernacular in Dante's Political Philosophy

Drawing primarily upon Dante’s three major philosophical treatises (De vulgari eloquentia, Convivio, and Monarchia), this essay explores how Dante’s ethico-political philosophy operates within the crucial tension between the phenomenology of time as the condition for the possibility of human moral development and yet also as, metaphysically speaking, the privation and imitation of eternity. I begin by showing that, in the De vulgari eloquentia, Dante’s understanding of the poetic and rhetorical function of the illustrious vernacular is tied to his political philosophy in a way that depends upon a rich but ultimately unresolved tension between (a) the demand that only an atemporal, unchanging vernacular would be suitable for the tasks of universal monarchy and (b) the recognition that only a temporal, localized, and changing illustrious vernacular could possibly bring about the existence of the universal monarchy. In the second half of the essay, I will turn to Dante’s treatment of the providential grounding for the independence of spiritual and temporal authority in Convivio and Monarchia. I will argue that Dante’s understanding of divine providence provides common justification for the temporal and spiritual authorities whose independence he otherwise insists upon. Finally, drawing on the letter to Cangrande della Scala (the authorship of which is disputed), I will discuss how, for Dante, the providential ground for the legitimacy of temporal authority can only be discerned through the allegorical interpretation of history itself. In light of my discussion of these themes in Dante’s political philosophy and its dependence on his understanding of divine providence, I will conclude with a brief reflection on how Dante’s understanding of divine providence might help us better appreciate important aspects of the neglected legacy of Renaissance humanism in the history of early modern philosophy

Paracompositionality, MWEs and Argument Substitution

Multi-word expressions, verb-particle constructions, idiomatically combining phrases, and phrasal idioms have something in common: not all of their elements contribute to the argument structure of the predicate implicated by the expression. Radically lexicalized theories of grammar that avoid string-, term-, logical form-, and tree-writing, and categorial grammars that avoid wrap operation, make predictions about the categories involved in verb-particles and phrasal idioms. They may require singleton types, which can only substitute for one value, not just for one kind of value. These types are asymmetric: they can be arguments only. They also narrowly constrain the kind of semantic value that can correspond to such syntactic categories. Idiomatically combining phrases do not subcategorize for singleton types, and they exploit another locally computable and compositional property of a correspondence, that every syntactic expression can project its head word. Such MWEs can be seen as empirically realized categorial possibilities, rather than lacuna in a theory of lexicalizable syntactic categories.Comment: accepted version (pre-final) for 23rd Formal Grammar Conference, August 2018, Sofi