Modular Logic Grammars

In Chapter 2 the translation relation between two languages was defined by means of isomorphic string grammars. Chapter 3 introduced the M-grammar formalism, which is used in the actual Rosetta system. M-grammars have a more sophisticated syntactic component than string grammars, but the semantic component and the way in which the translation relation is defined are essentially the same. For both types of grammars, two sentences s 1 and s 2 of languages L 1 and L 2 are considered translation-equivalent if they can be derived by isomorphic syntactic derivation trees, which implies that they share a semantic derivation tree.

A Logical Form (LF) is a syntactic structure that is interpreted by the semantic component. For a particular structure to be a possible LF it has to be possible for syntax to generate it and for semantics to interpret it. The study of LF must therefore take into account both assumptions about syntax and about semantics, and since there is much disagreement in both areas, disagreements on LF have been plentiful. This makes the task of writing a survey article in the field fairly difficult, a difficulty that is amplified by the amount of material that needs to be covered if the result is going to be in any way representative. My response to this difficulty is to limit my objectives. As a start, I will confine myself to issues relating to the syntactic positions of Quantificational Noun Phrases (QNPs) at LF and to various interpretive consequences. But even within these relatively narrow confines, I will not attempt anything close to a comprehensive survey. Instead my goal will be restricted to the presentation of one leading idea and to the discussion of some evidence that might bear on it. Much research on the nature of LF has consisted in attempts to account for the meaning of sentences containing QNPs:

The English noun phrase is exceedingly complex. The Head-word can be modified by a number of other grammatical elements such as determiners, intensifiers, adjectives, etc. These modifiers of the head-word are properly ordered and rule-governed. The purpose of this study, therefore, is to examine word order in the English noun phrase and show how this can pose a problem to the second language learner in the Nigeria situation. The study adopted the case study research design. The data for the study were collected through the test administered to two thousand final year students randomly selected from twenty government owned secondary schools in Port Harcourt, Rivers State, Nigeria. The theoretical framework employed was Rod Ellis procedural analysis of errors. The findings of this study reveal that learners experience some difficulties in the placement of modifiers in the English noun phrase. The study recommends that teachers should emphasize the established order of modifiers especially the pre-modifiers in the English noun phrase and where possible, use language games to teach the students to overcome the problem. The study concluded by noting that if serious attention is given to the order of pre-modifiers in the noun phrase, the problems students have in ordering words in the English noun phrase would be greatly reduced.

Combinatory Categorial Grammar (CCG) allows semantically equivalent alternate surface derivations typified by the sentence “Harry admires Louise,” as well as English noun phrases, to have all of the type-raised categories allowed by a full-blown morphological case system. Many critics have argued that this so-called spurious ambiguity makes CCG quite impracticable to apply to useful tasks such as parsing and question answering in open domains, regardless of its linguistic attractions. This chapter examines how CCG can be used for efficient natural language processing. It first considers algorithms that have formed the basis of a number of practical CCG parsers before turning to logical forms and how they are built with CCG. The chapter also discusses processing scope and pronominal reference in CCG, generation of strings from logical forms using CCG, the use of scope for rapid inference in support of question answering or textual entailment, and human sentence processing.

syntax is a semantic tree representation that lies between parse trees and logical forms. It abstracts away from word order and lexical items, but contains enough information to generate both surface strings and logical forms. Abstract syntax is commonly used in compilers as an intermediate between source and target languages. Grammatical Framework (GF) is a grammar formalism that generalizes the idea to natural languages, to capture cross-lingual generalizations and perform interlingual translation. As one of the main results, the GF Resource Grammar Library (GF-RGL) has implemented a shared abstract syntax for over 30 languages. Each language has its own set of concrete syntax rules (morphology and syntax), by which it can be generated from the abstract syntax and parsed into it. This paper presents a conversion method from abstract syntax trees to dependency trees. The method is applied for converting GF-RGL trees to Universal Dependencies (UD), which uses a common set of labels for different languages. The correspondence between GF-RGL and UD turns out to be good, and the relatively few discrepancies give rise to interesting questions about universality. The conversion also has potential for practical applications: (1) it makes the GF parser usable as a rule-based dependency parser; (2) it enables bootstrapping UD treebanks from GF treebanks; (3) it defines formal criteria to assess the informal annotation schemes of UD; (4) it gives a method to check the consistency of manually annotated UD trees with respect to the annotation schemes; (5) it makes information from UD treebanks available.

This paper aims to investigate the distribution and function of the determiners sē, sēo, þæt in Old English genitive noun phrases. The hypotheses presented stem from the analysis of the Old English version of Bede's "Historia Ecclesiastica Gentis Anglorum". Data shows, on the one hand, that determiners display a peculiar distribution, as their position varies according to the relative order of the genitive modifier and the head noun in genitive noun phrases, be it "genitive+noun" or "noun+genitive". On the other hand, their function does not seem to be as clear-cut as is usually described in grammar textbooks, since determiners appear to be used in a bridging context, oscillating between pragmatic or semantic definiteness. The discussion in this paper provides a functional description of determiners on the basis of the type of genitive noun phrase as a contribution to the debate on the status of determiners in Old English. Additionally, it provides a hypothesis concerning the apparent correlation between determiners and "head + modifier" structures where they appear to be six times as frequent as in "modifier + head": the hypothesis is that this correlation is not casual, but may have originated from appositive structures of the kind "Head-Noun+[DET+Adj/N]".

Logical Form in Linguistics

This study investigates second language acquisition of English noun phrases in discourse, examining the effect of discourse markedness and structural markedness on the development of noun phrase use. English L2 noun phrase forms are examined within three universal discourse contexts: current, known, and new reference to topics. The targeted noun phrases forms include ø anaphora, pronouns and nouns with markers of definiteness and indefiniteness, including left dislocation and existential phrases. Based on expectedness within discourse, the least marked discourse context is reference to a current topic, and the most marked context is the introduction of a new referent as topic. Based on formal complexity, ø anaphora is the least marked structural form, and left-dislocated and existential noun phrases are the most marked. Free production and elicited imitation recall tasks, involving picture sequences that manipulated the three discourse contexts, were used to test Japanese learners' acquisition of noun phrase forms. They were evaluated by comparison with NS production. The results support predictions that L2 learners distinguish between discourse contexts, acquiring more targetlike forms in the least marked context first, and that they acquire the least marked structural forms earlier than the more marked ones.

This researchaims to describe mixing code form of the post of facebook account Meme Manado Basudara. The object of this research mixing code form of the post of facebook account Meme Manado Basudara. The research method used is descriptive qualitative method. Data analysis techniques in this research are descriptive analysis and data collection techniques with 2 techniques, namely reading and note taking. Based on the analysis of the research, it was found that the forms of words consisting of nouns (nouns), adjectives (adjectives), verbs (verbs), adverbs (adverbs). The various forms of phrase codes were also found in this research, namely noun phrases, verb phrases and adjective phrases.There are mixing code form of words consisting of mixed forms of noun code (nouns) instead of 7 nouns consisting of 6 Indonesian nouns and 1 English noun. The mixing code form of adjective found 8 adjectives consisting of 6 Indonesian adjectives, 6 Indonesian adjectives and 2 English adjectives. The mixing code form of verbs (11 verbs), 11 verbs consisting of 6 Indonesian verbs, 5 verbs in English. The form of a mixture of adverb code that is 3 Indonesian adverb languages. The results of the research mixing code form of the post of facebook account Meme Manado Basudaraalso found mixed forms of phrase codes including 1 English noun phrase, 1 English verb phrase and 1 English adjective phrase.Keywords : mixed code, social media, ,meme

NOMINALIZATIONS IN ENGLISH have received much attention from transformational grammarians.' In recent years, the correct description of a particular type of English nominalization, known as the DERIVED NOMINAL, has been an issue in the controversy between interpretive semantics and generative semantics. The claim has been made in support of interpretive semantics that verbs derived transformationally from other verbs do not have corresponding derived nominals. I will show that for the class of causative verbs this claim is wrong. Interpretive semantics is a variant of the transformational theory of grammar developed by Noam Chomsky and bthers.2 It emphasizes the role of phrase structure rules and rules of semantic interpretation that apply to pairs of deep and surface phrase markers, and it reduces the role of transformations in grammatical descriptions.3 Generative semantics derives from the same transformational theory, but has rejected phrase structure rules, rules of semantic interpretation like those mentioned above, and the concept of deep structure as that point separating the syntactic and semantic components of the grammar, where all lexical items are inserted. No distinction between syntactic and semantic components is made in generative semantics, and lexical insertion is not restricted to one point in the grammar.4 Chomsky, who has been one of the foremost proponents of interpretive semantics, has claimed that derived nominals like its growth and their arrival constitute a part of English grammar that cannot be described transformationally.5 He supports this claim by contrasting such derived nominals

This research aims to discover the similarity and differences of Noun Phrase (NP) used in English and Indonesian sentences. This scientific writing used an instrument of report text as the reference to collect data. The report text was taken from a textbook of Developing English Competencies for senior high school. This research demonstrated that when English Noun Phrase was translated to Indonesian, there were changes in syntatic pattern, syntatic category, and meaning. Based on the research results, researchers found several similarities between Indonesian and English Noun Phrases. Similar parts, including head, determiner,and modifier, formed the Noun Phrase. However, there were also differences between them. English Noun Phrase was frequently expanded to the side of the head; meanwhile, in Indonesian, it was expanded to the back of the head. English Noun Phrase consists of a central-determiner (the, a, an); meanwhile, Indonesian Noun Phrase lacks it.

Combining biometric and symbolic models for customised, automated prosthesis design

It has been one of the strange and unexamined features of contemporary philosophy that philosophical as well as technical concern with the formal sciences — formal logic and mathematics, formal syntax and semantics — has been taken to be an ally of a positivistic, formalistic and (narrowly) analytic philosophical perspective. I believe that upon closer questioning, this alleged alliance breaks down, and the prima facie neutrality of the concern with formalism leaves room for a great diversity of philosophical standpoints — from a Platonic to a Kantian, to name two familiar contrasting positions. It is also a philosophically unexamined point of view, which requires that an understanding of the nature of the formal sciences must itself be formalistic, that you truely understand the nature of a formal discipline when you embed it in a meta — discipline of the same nature. There is certainly a sense of “understanding” in which this is the case. But there is a sense of “understanding”, a sense that is of central importance to philosophy — in which one can ask questions about the formal sciences which do not permit any non-trivially formalised answer.

LangPro is an automated theorem prover for natural language (https://github.com/kovvalsky/LangPro). Given a set of premises and a hypothesis, it is able to prove semantic relations between them. The prover is based on a version of analytic tableau method specially designed for natural logic. The proof procedure operates on logical forms that preserve linguistic expressions to a large extent. %This property makes the logical forms easily obtainable from syntactic trees. %, in particular, Combinatory Categorial Grammar derivation trees. The nature of proofs is deductive and transparent. On the FraCaS and SICK textual entailment datasets, the prover achieves high results comparable to state-of-the-art.

I show two limitations of multiplicative (or context-independent) sequent calculi: contraction can neither be restricted to atoms nor to the bottom of a proof tree. There is a a set of rules for classical propositional logic, system SKS [1], with two interesting properties: 1. Contraction can be restricted to atoms. As a consequence, no rule in system SKS requires the duplication of formulae of unbounded size. 2. Contraction can be restricted to the bottom of a proof. As a consequence, a proof in SKS can be separated into two phases (seen bottom-up): In the first phase atoms are duplicated and in the second phase all other rules are applied and the size of the frontier of the proof (in terms of number of atoms) does not increase. System SKS is not a sequent calculus but is presented in a more general formalism, the calculus of structures [2]. While the sequent calculus restricts the application of rules to the main connective of a formula, the calculus of structures is more expressive by admitting rules that can be applied anywhere deep inside formulae. This leads to the question whether the extra expressive power of the calculus of structures is needed to observe these properties, or whether they can be observed in sequent systems as well. This question seems quickly answered by sequent system G3cp [3] in which contraction is admissible and can thus trivially be restricted to atoms or to the bottom of a proof. However, the R∧-rule in G3cp is additive (or context-sharing), so none of the above mentioned interesting consequences for system SKS follow for G3cp. Even though contraction is admissible, formulae of unbounded size still have to be duplicated in the context of an additive R∧. The separation of a proof into two phases as in system SKS also is not observable in G3cp, simply because there is no rule that just duplicates formulae. To answer the question whether similar properties to those of system SKS can be achieved in sequent systems, I thus consider systems with a multiplicative R∧-rule. For the specific case of system GS1p [3], a Gentzen-Schutte formulation of classical logic shown in Fig. 1, I now prove by counterexample that it does not admit the properties of SKS. Atoms can be either positive or negative and are denoted by a or b. The negation of an atom a is denoted by ā and is again an atom. In a proof, contraction is considered to be at the bottom if there is no application of a rule different from contraction such that one of its premises is the conclusion of a contraction. An application of the contraction rule is considered atomic if its principal formula is an atom. Theorem 1. There is a sequent that is valid but for which there is no cut-free proof in GS1p with multiplicative context treatment in which all contractions are at the bottom. Ax A, Ā Γ,A ∆, Ā Cut Γ,∆ Γ,A,B R∨ Γ,A ∨B Γ,A ∆,B R∧ Γ,∆,A ∧B Γ,A,A RC Γ,A Γ RW Γ,A Fig. 1. GS1p with multiplicative context treatment Proof. Consider the following sequent: a ∧ a, ā ∧ ā . It suffices to show that a ∧ a, . . . , a ∧ a, ā ∧ ā, . . . , ā ∧ ā (for any number of occurrences of the formulae a ∧ a and ā ∧ ā) is not provable in GS1p without contraction and cut. The connective ∨ does not occur in the conclusion. Thus, the only rules that can appear in the proof are RW ,Ax and R∧. A proof has to have all branches closed with axioms A, Ā. Since no rule that may occur introduces new formulae, the only formula that can take the place of A in an axiom is the atom a. There can be no such proof since there is always one branch in the derivation tree in which there is at most one single atom, as is shown by induction on the derivation tree: Base Case There is only one branch in a ∧ a, . . . , a ∧ a, ā ∧ ā, . . . , ā ∧ ā and it contains at most one (that is, no) single atom. Inductive Case Weakening does not increase the number of single atoms. When a R∧ rule is applied, the context is split, so the only single atom that may occur in the conclusion goes to one branch. Choose the other branch, which has at most one (that is, exactly one) atom. Theorem 2. There is a sequent that is valid but for which there is no cut-free proof in GS1p with multiplicative context treatment in which all contractions are atomic.