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On the Relation Between Context and Sequence Unification
"... Both Sequence and Context Unification generalize the same problem: Word Unification. Besides that, Sequence Unification solves equations between unranked terms involving sequence variables, and seems to be appealing for information extraction in XML documents, program transformation, knowledge repre ..."
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Both Sequence and Context Unification generalize the same problem: Word Unification. Besides that, Sequence Unification solves equations between unranked terms involving sequence variables, and seems to be appealing for information extraction in XML documents, program transformation, knowledge representation, and rulebased programming. It is decidable. Context Unification deals with the same problem for ranked terms involving context variables, and has applications in computational linguistics and program transformation. Its decidability is a longstanding open question. In this work we study a relation between these two problems. We introduce a variant (restriction) of Context Unification, called LeftHole Context Unification (LHCU), to which Sequence Unification is Preduced: We define a partial currying procedure to translate sequence unification problems into lefthole context unification problems, and prove soundness of the translation. Furthermore, a precise characterization of the shape of the unifiers allows us to easily reduce LeftHole Context Unification to (the decidable problem of) Word Unification with Regular Constraints, obtaining then a new decidability proof for Sequence Unification. Finally, we define an extension of Sequence Unification (ESU) and, closing the circle, prove the inter Preducibility of LHCU and ESU.
Simplifying the signature in secondorder unification
, 2009
"... SecondOrder Unification is undecidable even for very specialized fragments. The signature plays a crucial role in these fragments. If all symbols are monadic, then the problem is NPcomplete, whereas it is enough to have just one binary constant to lose decidability. In this work we reduce SecondO ..."
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SecondOrder Unification is undecidable even for very specialized fragments. The signature plays a crucial role in these fragments. If all symbols are monadic, then the problem is NPcomplete, whereas it is enough to have just one binary constant to lose decidability. In this work we reduce SecondOrder Unification to SecondOrder Unification with a signature that contains just one binary function symbol and constants. The reduction is based on partially currying the equations by using the binary function symbol for explicit application @. Our work simplifies the study of SecondOrder Unification and some of its variants, like Context Unification and Bounded SecondOrder Unification.
Strategic choice during economic crisis: Domestic market position, . . .
 JOURNAL OF WORLD BUSINESS
, 2009
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On the complexity of Bounded SecondOrder Unification and Stratified Context Unification
"... Bounded SecondOrder Unification is a decidable variant of undecidable SecondOrder Unification. Stratified Context Unification is a decidable restriction of Context Unification, whose decidability is a longstanding open problem. This paper is a join of two separate previous, preliminary papers on ..."
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Bounded SecondOrder Unification is a decidable variant of undecidable SecondOrder Unification. Stratified Context Unification is a decidable restriction of Context Unification, whose decidability is a longstanding open problem. This paper is a join of two separate previous, preliminary papers on NPcompleteness of Bounded SecondOrder Unification and Stratified Context Unification. It clarifies some omissions in these papers, joins the algorithmic parts that construct a minimal solution, and gives a clear account of a method of using singleton tree grammars for compression that may have potential usage for other algorithmic questions in related areas.
Networks of morphological relations
"... Whole Word Morphology does away with morphemes, instead representing all morphology as relations among sets of words, which we call lexical correspondences. This paper presents a more formal treatment of Whole Word Morphology than has been previously published, demonstrating how the morphological ..."
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Whole Word Morphology does away with morphemes, instead representing all morphology as relations among sets of words, which we call lexical correspondences. This paper presents a more formal treatment of Whole Word Morphology than has been previously published, demonstrating how the morphological relations are mediated by unification with sequence variables. Examples from English are presented, as well as Eskimo, the latter providing an example of a highly complex polysynthetic lexicon. The lexical correspondences of Eskimo are operative through their interconnection in a network using a symmetric and an asymmetric relation. Finally, a learning algorithm for deriving lexical correspondences from an annotated lexicon is presented. 1
J Autom Reasoning (2014) 52:155–190 DOI 10.1007/s1081701392856 Antiunification for Unranked Terms and Hedges
"... © The Author(s) 2013. This article is published with open access at Springerlink.com Abstract We study antiunification for unranked terms and hedges that may contain term and hedge variables. The antiunification problem of two hedges s̃1 and s̃2 is concerned with finding their generalization, a he ..."
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© The Author(s) 2013. This article is published with open access at Springerlink.com Abstract We study antiunification for unranked terms and hedges that may contain term and hedge variables. The antiunification problem of two hedges s̃1 and s̃2 is concerned with finding their generalization, a hedge q ̃ such that both s̃1 and s̃2 are instances of q ̃ under some substitutions. Hedge variables help to fill in gaps in generalizations, while term variables abstract single (sub)terms with different top function symbols. First, we design a complete andminimal algorithm to compute least general generalizations. Then, we improve the efficiency of the algorithm by restricting possible alternatives permitted in the generalizations. The restrictions are imposed with the help of a rigidity function, which is a parameter in the improved algorithm and selects certain common subsequences from the hedges to be generalized. The obtained rigid antiunif ication algorithm is further made more precise by permitting combination of hedge and term variables in generalizations. Finally, we indicate a possible application of the algorithm in software engineering. This research has been partially supported by the Spanish Ministerio de Economa
On the Limits of SecondOrder Unification
"... SecondOrder Unification is a problem that naturally arises when applying automated deduction techniques with variables denoting predicates. The problem is undecidable, but a considerable effort has been made in order to find decidable fragments, and understand the deep reasons of its complexity. Tw ..."
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SecondOrder Unification is a problem that naturally arises when applying automated deduction techniques with variables denoting predicates. The problem is undecidable, but a considerable effort has been made in order to find decidable fragments, and understand the deep reasons of its complexity. Two variants of the problem, Bounded SecondOrder Unification and Linear SecondOrder Unification –where the use of bound variables in the instantiations is restricted–, have been extensively studied in the last two decades. In this paper we summarize some decidability/undecidability/complexity results, trying to focus on those that could be more interesting for a wider audience, and involving less technical details. 1