BAR-HILLEL, Y., On Categorial and Phrase Structure Grammars, in: Y. Bar-Hillel (ed.), Language and Information, Addison-Wesley, Reading 1964.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....are so similar that they can only be distinguished by the use of syntactic information. We compute the syntactic structure of a question by using an efficient deductive object oriented parsing algorithm [12] which operates on the basis of a powerful extension of the categorial grammar formalism [2]. The result of the syntactic analysis is used to distinguish between the similar semantic categories. This is achieved by applying syntactic disambiguation rules derived from the XSE tree to the resulting parsing tree. If the syntactic disambiguation rule is satisfied, the semantic category can ....

BAR-HILLEL, Y., On Categorial and Phrase Structure Grammars, in: Y. Bar-Hillel (ed.), Language and Information, Addison-Wesley, Reading 1964.

....are so similar that they can only be distinguished by the use of syntactic information. We compute the syntactic structure of a question by using an efficient deductive object oriented parsing algorithm [17] which operates on the basis of a powerful extension of the categorial grammar formalism [2]. Input: douteki roudingu no chousho wa nani ka. What is the strong point of dynamic loading DFL: surface form category subcategory deep form unknown kanji unknown katakana particle modifier noun strong point particle topic pronoun interrogative what particle question punctuation ....

Y. Bar-Hillel, On categorial and phrase structure grammars, in: Y. Bar-Hillel, ed., Language and Information (Addison-Wesley, Reading, 1964).

....Categorial Grammar (CG) is an unconventional grammar theory which assigns all grammar rules to the dictionary entries, making any additional explicit grammar superfluous. There exist two kinds of categories: basic categories (e.g. S, N) and complex categories (e.g. NP N, S NP) The original theory [6] consists of only two combinatory rules for the formation of complex categories (A, B representing grammatical categories) Forward functional application: A B B A Backward functional application: B A B A The two combinatory rules were extended by Steedman [7,8] by four rules for functional ....

Y. Bar-Hillel. On Categorial and Phrase Structure Grammars. In Language and Information, Reading: Addison-Wesley, 1964.

....grammar 23 8. Conjoinable types in the Lambek calculus 24 9. Multiplicative cyclic linear logic 26 Index 30 References 31 Introduction The question about the position of categorial grammars in the Chomsky hierarchy arose in late 1950s and early 1960s. In 1960 Bar Hillel, Gaifman, and Shamir [1] proved that a formal language can be generated by some basic categorial grammar if and only if the language is context free. They conjectured (see also [7] that the same holds for Lambek grammars, i.e. for categorial grammars based on a syntactic calculus introduced in 1958 by J. Lambek [10] ....

....over the Lambek calculus L. 9.2. Free group interpretation of CLL formulas. Definition 9.2. The free group interpretation of CLL formulas (denoted by [ is the following natural mapping of formulas and their finite sequences into the group F(Var) LAMBEK CALCULUS AND FORMAL GRAMMARS 27 [[1]] # [ #] # [ p i ] p i [ p # i ] p 1 i [ A.B] A] B] AOB] A] B] A 1 . An ] A 1 ] A n ] Lemma 9.3. For any formula A # Fm( O, 1, #) A] # #A#. Proof. By induction on the construction of A. Lemma 9.4. If a sequent # # is ....

Y. Bar-Hillel, C. Gaifman, and E. Shamir, On categorial and phrase structure grammars, Bull. Res. Council Israel F 9 (1960), 1--16.

....Grammars Radim B elohl avek Abstract. We introduce a new way to describe formal languages. Algebra grammar is a generalization of categorial grammar introduced in [1]. It is shown that both regular and context free languages can be represented by certain types of algebra grammars. Keywords: formal language, grammar, variety of algebras The aim of this short paper is to show a new way to describe formal languages. Formal languages have been studied by many ....

....that both regular and context free languages can be represented by certain types of algebra grammars. Keywords: formal language, grammar, variety of algebras The aim of this short paper is to show a new way to describe formal languages. Formal languages have been studied by many authors. In [1], the authors proposed the so called categorial grammars which have applications in study of natural languages. Categorial grammars are based on the concept of category which can be considered as a syntactical part of a sentence. It is proved that every categorial grammar represents a context free ....

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Bar-Hillel Y., Gaifman C., Shamir E.: On categorial and phrasestructure grammars, Bull. Res. Counc. of Israel, Vol. 9F, 1960

....was first adopted in the 3 Capital letters represent meta phonemes which will be explained in Section 3.3. 8 1960s. The reason for this renewed interest was that categorial grammar lends itself naturally to the kind of semantic types which can be put in correspondence with syntactic types. Bar Hillel, Gaifman, and Shamir (1960) proved that a pure categorial grammar is weakly equivalent to a context free grammar. CGs are lexicalist formalisms, that is most of the information is put into the lexicon instead of having them in the grammar. A pure categorial grammar has the following four characteristics: a) There is a ....

Bar-Hillel, Y., C. Gaifman, and E. Shamir. 1960. On categorial and phrase structure grammars. The Bulletin of the Research Council of Israel, 9F:1--16.

....is also defined, since h is a function. 10 For readability, I use here a notation of the form (w(w 1 , w n ) as an abbreviation for g( g (g (w, w 1 ) w 2 ) w n ) 11 The first substantial refinements or extensions of the pure categorial paradigm go back to the work of Bar Hillel (1960) and Geach (1970) Some indications of the current trends may be found in Bach (1984) Oehrle, Bach and Wheeler, eds. 1988) and Buszkowski, Marciszewski and van Benthem, eds. 1988) VARIABLE BINDERS AS FUNCTORS 14 12 Certain aspects of the proposed account might still sound unpalatable. For ....

Bar-Hillel Y. (1960), `On Categorial and Phrase-Structure Grammars', Bulletin of the Research Council of Israel 3, 1-16.

....is said to be a Structural Example for G iff there exists a syntactic tree generating the corresponding sentence in G so that the composition is obtained by replacing every non terminal symbol of this syntactic tree by the symbol class of the rule used to rewrite it. Example 1 : It is well know ([1]) that AB Categorial Grammars are equivalent with context free grammars, so the previous definitions can straightforwardly be adapted to this class. Let us define a basic AB Categorial Grammar G for the analysis of a small subset of English. Let S = a, man, John, Mary, runs, loves be the ....

Y. Bar Hillel, C. Gaifman, E. Shamir, "On Categorial and Phrase Structure Grammars", Bulletin of the Research Council of Israel, 9F, p116, 1960.

....[12] 12 The point is due to Schnfinkel [16] and reflects the set theoretic isomorphism between A B 1 B 2 . B n and ( A B 1 ) B 2 ) B n . 13 See Lesniewski [9] and Ajdukiewicz [1] 14 See [21] for the details. 15 Ajdukiewicz [1] p. 231. 16 Compare Bar Hillel et al. [2]. 17 Compare Cresswell [4] pp. 266 67. 18 See note 1 above. 19 To my knowledge, the intensional character of variable binders was first pointed out in Lewis [7] though the 1986 Postscript [8] marks a change of view recommending to treat variable binding outside the categorial framework, in ....

Bar-Hillel, Y., Gaifman C., Shamir E., `On Categorial and Phrase-Structure Grammars', The Bulletin of the Research Council of Israel 3 (1960), 1-16.

....exists an LCG, L, such that L(L) S. The proof presented in this paper will prove the only if direction only. The weak equivalence of Ajdukiewicz Categorial Grammar (ACG, basically, LCG without the introduction rules) to CFG s was first proven by Gaifman, and later, more elegantly, by Shamir [2], and even later, even more elegantly by Gladkij [9] The only if direction of Shamir s proof showed how to reduce a Chomsky Normal Form CFG to a kind of ACG, called a Restricted Categorial Grammar (RCG) which restricted the forms of categories it could assign in its initial assignment ....

Bar-Hillel, Y., Gaifman, C., and Shamir, E., 1960. On Categorial and Phrase Structure Grammars. In The Bulletin of the Research Council of Israel.

.... Lambek Grammars to Basic Categorial Grammars Wojciech Buszkowski Faculty of Mathematics and Computer Science Adam Mickiewicz University Pozna n Poland Abstract Pentus [24] proves the equivalence of LCG s and CFG s, and CFG s are equivalent to BCG s by the Gaifman theorem [1]. This paper provides a procedure to extend any LCG to an equivalent BCG by affixing new types to the lexicon; a procedure of that kind was proposed as early, as Cohen [12] but it was deficient [4] We use a modification of Pentus proof and a new proof of the Gaifman theorem on the basis of ....

....c; Y b XY (bna)Z c ( 1) XaZ c; Y b X(a=b)Y Z c. The sequent X a is derivable in B if, and only if, X reduces to a by the standard reduction procedure based on the rules: Rn) b(bna) a (R ) a=b)b ) a, and consequently, BCG s are precisely categorial grammars in the sense of [1]. Lambek Categorial Grammars (LCG s) are based on the system L equal to B enriched with additional rules: n2) bX a X bna ( 2) Xb a X a=b, where X is nonempty (dropping this constraint yields a stronger system L1) The full Lambek Calculus admits types with product and can be ....

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Y. Bar-Hillel, C. Gaifman and E. Shamir, On categorial and phrase structure grammars, Bull. Res. Council Israel F 9, (1960), 155-166.

....feasible, this lexical entry is dropped. We restrict the grammars to lexicalized ones. A grammar is lexicalized if for every local syntax tree there is at least one preterminal leaf, cf. Schabes and Waters, 1993 ] Note that lexicalization does not affect the expressibility of the grammar [ Bar Hillel et al. 1960 ] Schabes and Waters, 1993 ] However, the generation algorithm turns much simpler and hence more efficient. There is no need for a transitive link relation, since a goal can match immediately the mother node of a preterminal. The lexicon access and the headcorner completion step can be ....

Yehoshua Bar-Hillel, Chaim Gaifman, and E. Shamir. On categorial and phrase structure grammars. Bull. Res. Council Israel, Sec. F., 9:1--16, 1960.

....and languages generated by CGs based on other TRSs with those levels of the hierarchy which are considered as the best approximations to the position of natural languages. The first result which established the generative power of CGs concerned grammars based on ABH o (ABH o grammars) In Bar Hillel, Gaifman and Shamir 1960 the following theorem was proved: Theorem 1. ABH o grammars generate precisely the class of CF languages. In the above paper a hypothesis was made according to which the class of languages generated by L o grammars coincided with the class of CFlanguages as well. Despite intense attempts ....

Bar-Hillel, Y., Gaifman C. and Shamir, E. 1960. "On categorial and phrase structure grammars". Bulletin Res. Council Israel F9: 1--16.

....from the fact that the emptiness problem for the intersection of two context free languages is undecidable. Given two context free grammars G 1 ; G 2 , one constructs Basic Categorial Grammars G 0 1 ; G 0 2 such that L(G 1 ) L(G 0 1 ) and L(G 2 ) L(G 0 2 ) the Gaifman theorem; see [1]) Recall that, for a categorial grammar G, L(G) TG (S) where S is a distinguished atomic type (the principal type) We make the atomic types involved in G 0 1 different from those involved in G 0 2 . Let S; S 0 be the principal types of G 0 1 ; G 0 2 , respectively. In the initial ....

Y. Bar-Hillel, C. Gaifman and E. Shamir, On categorial and phrase structure grammars, Bulletin Res. Council Israel, F 9, (1960), 155-166.

.... B B A for A B N and B A N respectively and also every rule of the form A a for A f(a) and a S. It can be noticed that G is in Chomsky Normal Form. As the simulation is also possible in the other direction, the class of languages recognized by CCGs is the class of context free languages ([Bar Hillel 60]) CCGs are very lexically oriented as grammatical information are entirely supported by the categories associated with each word. They are thus very well adapted to natural languages ( Oehrle 88] 6 2.2 Learning from Structural Examples As the Classical Positive Problem has been proven ....

....has then mainly been studied in the context of Structural Examples of the kind given in Example 4, i.e. skeletons. This approach was first exemplified by Sakakibara who proposed algorithms to build a tree automaton (and consequently a corresponding context free grammar) from such skeletons ( Sakakibara 90, 92] Others have developed similar ideas ( M kinen 92a, 92b] Sempere Nagaraja 98] The Problem with Positive Structural Examples has also been adapted to the formalism of CCG, taking into account Structural Examples of the kind given in Example 5. In this way, Kanazawa ( Kanazawa 96] ....

: Y. Bar-Hillel, C. Gaifman, E. Shamir, "On Categorial and Phrase Structure Grammars", Bulletin of the Research Council of Israel. 9F, p1-16, 31

....being that these arguments must be attached in the order in which they occur on the subcategorization list. While our notation follows the usage of HPSG and Unification Categorial Grammar (Calder et al. 1988) it should be clear how it relates to more traditional categorial grammar notation (see Bar Hillel et al. 1960). We assume the following schematic phrase structure rule which allows heads to combine with a single complement: b[c 1 ; c n ] Gamma b[c 0 ; c n ] c 0 (1) In most categorial grammars and in HPSG, there are rules in which the complement category precedes the head, but we do not ....

....context free grammar. This is because only the finitely many subcategories of the lexical categories may ever be used in a derivation and thus only finitely many instances of the application scheme are necessary for a finite categorial lexicon. Somewhat surprisingly, the converse result also holds (Bar Hillel et al. 1960); every context free language is generated by some categorial grammar in the form we have presented. This latter result can be deduced from the fact that every context free language can be expressed with a Greibach normal form grammar where every production is of the form C 0 Gamma aC 1 Delta ....

Bar-Hillel, Y.; C. Gaifman and E. Shamir 1960 On categorial and phrase structure grammars.

....are assigned to quantifiers to account for their distribution. In this way it is similar to the approach to quantification 11 Both the simple categorial grammar with only application, and Lambek s categorial grammars, have both been shown to generate all and only the context free languages [Bar Hillel, Gaifman and Shamir 1960, Pentus 1992] even if restricted to only one variety of slash, either forward or backward. 16 bob carpenter Scope Left Gamma 1 ; B: x; Gamma 2 ) A: fi r Gamma 1 ; A B: ff; Gamma 2 ) A: ff(x:fi) x fresh] Scope Right l B: fi ) A B: x:x(fi) Figure 9: Sequent Presentation of Scoping ....

Bar-Hillel, Y., C. Gaifman, and E. Shamir, 1960, On categorial and phrase structure grammars. Bulletin of the Research Council of Israel F 9, 1--16.

....in categories. This means that any finite categorial lexicon, together with the application schemes, will determine a grammar structurally equivalent to a context free grammar. Somewhat surprisingly, the converse to this result also holds in the weak generative case, as was proved by Gaifman (Bar Hillel, Gaifman and Shamir 1960). That is, every context free language (set of expressions generated by a finte contextfree grammar) can be generated by a categorial grammar applying the application schemes to a finite lexicon. Consequently, evidence beyond simple acceptability of sentences must be employed to distinguish ....

Bar-Hillel, Y., C. Gaifman, and E. Shamir, 1960. On categorial and phrase structure grammars.

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Bar-Hillel, Y., C. Gaifman and E. Shamir, `On categorial and phrase structure grammars', The Bulletin of the Research Council of Israel 9F, 1960, 16

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Bar-Hillel, Y., C. Gaifman and E. Shamir, `On categorial and phrase structure grammars', The Bulletin of the Research Council of Israel 9F, 1960, 16

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Y. Bar Hillel, C. Gaifman, and E. Shamir. 1960. On categorial and phrase structure grammars.

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Y. Bar-Hillel, C. Gaifman, and E. Shamir. On categorial and phrase structure grammars. In Bulletin of the Research Council of Israel 9F, 1-16.

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