Clause Head Research Articles

Reconstructing a single-head formula to facilitate logical forgetting

Abstract Logical forgetting is removing some variables from a formula while maintaining its consequences on the remaining variables. This removal may require exponential time on arbitrary propositional Horn formulae, but it only takes polynomial time on single-head propositional definite Horn formulae. Single-head means that no variable is the head of multiple clauses. An algorithm to make a formula single-head if possible is shown. It enlarges the set of formulae admitting polynomial-time forgetting by making them single-head if possible and then running the usual algorithm for forgetting.

Changes in the proverb formula in Finnish Bibles from 1642 to 1992

Abstract The article studies a subtype of the Finnish generalizing relative clause, referred to as the proverb formula. A generalizing relative clause refers to any person who fills the described condition. The proverb formula is used frequently in the Finnish translations of the Bible in the Book of Proverbs. The study examines two aspects that vary in this structure in Finnish editions from 1642 to 1992: the head pronoun of the relative clause and the order of the relative clause and the main clause. In the oldest of the studied translations, the most frequent one variant or the proverb formula begins with the relative clause, and the relative clause head in the main clause is a personal pronoun (hän). For the order of the structure, a clear model is found in the source texts of the translation. In later editions, personal pronoun heads were eliminated. Interestingly, they are not replaced with demonstrative heads, which would follow the most frequent proverb formula structure in Finnish vernacular and would also be recommenced by grammar guides. Instead, a variant with omission of the head pronoun gains in frequency. Variations within the proverb formula increase when the order with the main clause preceding the relative clause gains in frequency. The preference for omission of the head pronouns is not easily explainable. The article proposes that this variant was a conscious stylistic choice for solemn, biblical language.

Analyzing Errors Made by Libyan Students When Learning Nominal Clauses

This study aims at investigating the errors Libyan students commit when learning English nominal clauses. In order to study these errors a ten-item test was designed and administered to fifteen students enrolled at the English department at the faculty of Arts and Science-Almarj. The data collected shows that participants have trouble in producing English nominal clauses. Their major difficulties lie in the area of nominal clause heads, pronoun retention, verb phrase, wrong clause choice, preposition, omission of subjects and adjacency errors. Additionally, the study provides suggestions for teaching English nominal clauses.

A Logical Characterization of the Preferred Models of Logic Programs with Ordered Disjunction

AbstractLogic programs with ordered disjunction (LPODs) extend classical logic programs with the capability of expressing alternatives with decreasing degrees of preference in the heads of program rules. Despite the fact that the operational meaning of ordered disjunction is clear, there exists an important open issue regarding its semantics. In particular, there does not exist a purely model-theoretic approach for determining the most preferred models of an LPOD. At present, the selection of the most preferred models is performed using a technique that is not based exclusively on the models of the program and in certain cases produces counterintuitive results. We provide a novel, model-theoretic semantics for LPODs, which uses an additional truth value in order to identify the most preferred models of a program. We demonstrate that the proposed approach overcomes the shortcomings of the traditional semantics of LPODs. Moreover, the new approach can be used to define the semantics of a natural class of logic programs that can have both ordered and classical disjunctions in the heads of clauses. This allows programs that can express not only strict levels of preferences but also alternatives that are equally preferred.

Pronominally headed relative clauses in early English

Present-day English is unlike Old English in not using singular demonstrative pronouns with anaphoric reference to human beings. This article adds to the contributions of Cole (2017) and Los & van Kemenade (2018) in our understanding of the factors determining the choice between personal and demonstrative pronouns in Old English by documenting the hitherto unexamined use of these pronouns as heads of relative clauses. It also traces how the singular demonstrative pronouns referring to humans retreated as heads of relative clauses in Early Middle English. A corpus-based study shows that third-person personal pronouns were unusual as heads of relative clauses in Old English and normally referred to specific individuals, while demonstratives were the pronouns of choice for generic reference but could also refer to specific individuals. The increased use of personal pronouns for generic reference is well underway in Early Middle English. While the retreat of the singular demonstrative pronouns to refer to humans in Early Middle English seems to have some connection with the reduced marking of feature distinctions in that period, a simple explanation in terms of loss of gender is untenable.

Unforced Revision in Processing Relative Clause Association Ambiguity in Japanese: Evidence Against Revision as Last Resort.

The current study tackles a long standing question of whether comprehenders perform structural revision when it is not forced by grammar or not. Using an eye-tracking reading paradigm, we addressed this issue by making use of global structural ambiguity in Japanese. Our results show that comprehenders initially associate a relative clause with the first potential head noun and that they revise this analysis when the second noun is lexico-semantically possible as the relative clause head, but do not when it is impossible. The results are incompatible with the Revision as Last Resort hypothesis. Instead, they support the parsing with unforced revision that is immediately sensitive to lexical properties. We argue that our results cannot be accounted for by serial modular processing models but that they can be explained by ranked-parallel interactive processing models. Furthermore, we propose that head-finality is a key factor involved in the availability of unforced revision.

Elicited production of relative clauses in German: Evidence from typically developing children and children with specific language impairment

We elicited the production of various types of relative clauses in a group of German-speaking children with specific language impairment (SLI) and typically developing controls in order to test the movement optionality account of grammatical difficulty in SLI. The results show that German-speaking children with SLI are impaired in relative clause production compared to typically developing children. The alternative structures that they produce consist of simple main clauses, as well as nominal and prepositional phrases produced in isolation, sometimes contextually appropriate, and sometimes not. Crucially for evaluating the movement optionality account, children with SLI produce very few instances of embedded clauses where the relative clause head noun is pronounced in situ; in fact, such responses are more common among the typically developing child controls. These results underscore the difficulty German-speaking children with SLI have with structures involving movement, but provide no specific support for the movement optionality account.

Effects of punctuation on the processing of temporarily ambiguous sentences in Japanese

This study explored the effects of comma insertion on the processing of garden path sentences in Japanese. In two experiments, participants read relative clause sentences containing two ambiguities: single versus relative clause and early-opening (EO) versus late-opening (LO) left clause boundaries. EO sentences were presented with or without a comma compatible with an EO boundary in Experiment 1 and, in Experiment 2, with an LO boundary. The results showed that the comma, whether compatible or incompatible with the correct clause boundary, decreased reading time for the relative clause's head noun, indicating that a comma helps readers avoid or recover from garden paths caused by relative clause structures. Conversely, a comma incompatible with a clause boundary increased processing costs of second ambiguity resolution (EO vs. LO). We concluded that punctuation affects processing of temporary ambiguity in Japanese as in languages with stricter punctuation rules; furthermore, readers depend strongly on punctuation for online processing of whole sentence structures. We also discuss the relationship between punctuation and (implicit) prosody.

Effects of punctuation on the processing of temporarily ambiguous sentences in Japanese

AbstractThis study explored the effects of comma insertion on the processing of garden path sentences in Japanese. In two experiments, participants read relative clause sentences containing two ambiguities: single versus relative clause and early‐opening (EO) versus late‐opening (LO) left clause boundaries. EO sentences were presented with or without a comma compatible with an EO boundary in Experiment 1 and, in Experiment 2, with an LO boundary. The results showed that the comma, whether compatible or incompatible with the correct clause boundary, decreased reading time for the relative clause's head noun, indicating that a comma helps readers avoid or recover from garden paths caused by relative clause structures. Conversely, a comma incompatible with a clause boundary increased processing costs of second ambiguity resolution (EO vs. LO). We concluded that punctuation affects processing of temporary ambiguity in Japanese as in languages with stricter punctuation rules; furthermore, readers depend strongly on punctuation for online processing of whole sentence structures. We also discuss the relationship between punctuation and (implicit) prosody.

A constraint-based approach to solving games on infinite graphs

We present a constraint-based approach to computing winning strategies in two-player graph games over the state space of infinite-state programs. Such games have numerous applications in program verification and synthesis, including the synthesis of infinite-state reactive programs and branching-time verification of infinite-state programs. Our method handles games with winning conditions given by safety, reachability, and general Linear Temporal Logic (LTL) properties. For each property class, we give a deductive proof rule that --- provided a symbolic representation of the game players --- describes a winning strategy for a particular player. Our rules are sound and relatively complete. We show that these rules can be automated by using an off-the-shelf Horn constraint solver that supports existential quantification in clause heads. The practical promise of the rules is demonstrated through several case studies, including a challenging "Cinderella-Stepmother game" that allows infinite alternation of discrete and continuous choices by two players, as well as examples derived from prior work on program repair and synthesis.

Logical foundations for more expressive declarative temporal logic programming languages

In this article, we present a declarative propositional temporal logic programming language called TeDiLog that is a combination of the temporal and disjunctive paradigms in logic programming. TeDiLog is, syntactically, a sublanguage of the well-known Propositional Linear-time Temporal Logic (PLTL). TeDiLog allows both eventualities and always-formulas to occur in clause heads and also in clause bodies. To the best of our knowledge, TeDiLog is the first declarative temporal logic programming language that achieves this high degree of expressiveness. We establish the logical foundations of our proposal by formally defining operational and logical semantics for TeDiLog and by proving their equivalence. The operational semantics of TeDiLog relies on a restriction of the invariant-free temporal resolution procedure for PLTL that was introduced by Gaintzarain et al. in [2013]. We define a fixpoint semantics that captures the reverse (bottom-up) operational mechanism and prove its equivalence with the logical semantics. We also provide illustrative examples and comparison with other proposals.

Overt Degree Arguments as Internal Heads of Relative Clauses of Degree

Overt Degree Arguments as Internal Heads of Relative Clauses of Degree

Hinuq verb forms and finiteness

This paper offers a comprehensive account of the verbal morphology in the Nakh-Daghestanian (or Northeast Caucasian) language Hinuq. As typical of the languages of that part of the world, Hinuq has a rich inventory of verbal inflectional suffixes, giving rise to verb forms with only verbal properties, and other verb forms lacking some verbal properties and having adjectival, adverbial or nominal properties instead. I argue that all Hinuq verb forms can be divided into two groups along the lines of their usage as heads of independent or dependent clauses. Furthermore, I demonstrate that some verb forms, which at first glance seem to violate this classification, synchronically represent different verb forms that can clearly be distinguished functionally and partially also on formal grounds. The paper also contributes to the actual discussion of the notion ‘finiteness’ and its applicability to Nakh-Daghestanian languages.

Small Clause as Unified TP-AgrP Structure

This paper is to defend for the unified clause structure in which nonfinite clauses including ECM and small clauses are all analyzed as constituents formed by the combination of two functional categories of TP and AgrP. The main purpose of the unified TP-AgrP approach is to simplify and generalize the various clause structures. For this, I propose the verbal predication mediated by functional heads and copulars. In verbal predication mediated by copulars, the small clause subject occurs in the Spec(TP) position and the small clause predicate is AgrP with the head Agr containing a predication operator or a predicate particle that turns small clause predicate into a predicate, and copulars move from VP to the predicational phrase head, Agr. In this proposal, the structure of the small clause parallels to that of infinitival ECM clause so that both clauses are proposed to be TP-AgrP. Accordingly, the parallel interpretations of ECM and small clauses can be explained by parallel structures. In a unified TP-AgrP structure, we can uniformly say that T is the head of finite clauses as well as infinitival clauses including ECM and small clauses. The small clause predicate is the verbal predication, so it is different from non-verbal predication. Therefore, the proposed verbal predication gives rise to satisfactory solutions to the problems previously raised by non-verbal predication. The proposed uniform structure TP-AgrP also explains the different behavior in predicate raising of ECM and small clauses with the argument that predicate raising is allowed only to A`-position. (Hanbat National University)

Disambiguating Information and Memory Resources in Children’s Processing of Italian Relative Clauses

We investigated the role of number agreement on verb and of animacy in the comprehension of subject and object relative clauses in 51 monolingual Italian-speaking children, mean age 9:33, tested through a self-paced listening experiment with a final comprehension question. A digit span test and a listening span test were also administered to examine the role of memory in comprehension. Subject relative clauses were easier to comprehend than object relative clauses; animacy of the relative clause head improved comprehension of object relative clauses; memory, as measured by the digit span test, modulates comprehension of object relative clauses, both with animate and inanimate heads, as shown in response accuracy. Although all children process number agreement morphology on the verb, only some perform a correct reanalysis, as shown by the accuracy measures.We argue that number agreement disambiguation is particularly taxing for children, as it provides a negative symptom in the sense of Fodor and Inoue (J Psycholinguist Res 29(1):25–36, 2000)and reanalysis requires them to hold two dependencies in memory.

The syntax of wek (‘which’) and zuk (‘such’) in West Flemish

This paper discusses the derivation of WF nominal constructions containing interrogative wek ‘which’ and demonstrative zuk ‘such’. Wek and zuk are often followed by what looks like a singular indefinite article, even when they associate with plural or non-count nouns. This use of the article is referred to as the spurious article (Bennis et al., 1998). It is proposed that wek and zuk originate as the (XP) predicates of a DP-internal small clause and undergo predicate inversion (cf. Bennis et al., 1998). The head of this small clause incorporates to a higher functional head for reasons of domain extension. The ‘spurious’ article en ‘a’ spells out this small clause head. To account for the data in which prenominal zuk co-occurs with the negative determiner geen and the obligatory absence of spurious en it is proposed that in addition to inverting with the subject of the small clause as an XP, zuk may also invert with the subject by head-movement. In the latter case, spurious en will not be required hence impossible. The same account applies to some patterns with wek. When moved as heads, zuk and wek are structurally deficient and need to incorporate to a lexical host.

Uniformity and diversity in the syntax of evaluative vocatives

This article investigates the internal syntax of evaluative vocative expressions (e.g., You idiot!). This construction superficially consists of a second person pronoun and an epithet noun. It turns out that this construction type has different morphosyntactic manifestations across languages/dialects (abstractly: youNOM idiot!; youACC/OBL idiot!; your idiot!). The paper aims at giving a uniform account for the ‘underlying’ syntax of this construction type. It is argued that this construction has the ‘underlying’ syntax of a possessive noun phrase. More particularly, the second person pronoun starts out as (part of) a PP-predicate and undergoes leftward predicate displacement within the vocative noun phrase. The major dimensions of (morpho)syntactic diversity are related to the following properties: (1) the nature of the predicate displacement operation involved (i.e., predicate inversion and/or predicate fronting); (2) the overtness versus covertness of the small clause head X, which is part of the vocative expression; (3) the case form of the second person pronoun. According to the structural analysis proposed in this article, evaluative vocative expressions form a further illustration of the structural uniformity that is hidden behind superficial diversity.

Reconstruction in relative clauses and the copy theory of traces*

In this paper, after discussing the status of the copy theory of traces in the current formulation of the minimalist program and the evidence for the “No-Tampering” Condition from which the copy theory of traces follows, I focus on a specific case study, namely reconstruction effects concerning the head of a relative clause. The common wisdom in the literature is that reconstruction of the relative clause head can be observed by using variable binding as a diagnostic, while the diagnostic based on Condition C gives opposite results. This split has led some researchers to propose that relative clauses are structurally ambiguous, because they would receive both a raising analysis (which explains variable binding reconstruction) and a non-raising analysis (which explains the absence of Condition C reconstruction). One of the goals of this paper is showing that it is not necessary to postulate that relative clauses are structurally ambiguous. In order to do that, I first show that the description in the literature is partly inaccurate. If some methodological problems raised by the use of transitive nouns are avoided, it can be shown that variable binding reconstruction occurs only when the relative clause modifies the subject of an equative sentence. This suggests that variable binding reconstruction of the relative clause head is not an ordinary case of reconstruction like the one found in canonicalwhchains but should be treated as a case of indirect binding, which is known to be sensitive to the identificational (as opposed to predicational) character of the sentence. I then show that, if this perspective is taken, the absence of Condition C effects can be explained without positing a structural ambiguity. The final result of the investigation is that, despite the initially puzzling evidence, the copy theory of traces can successfully explain the reconstruction pattern of the relative clause head.

Agreement checking in comprehension: evidence from relative clauses.

Work on agreement processing in comprehension in English has provided evidence that the plural feature is "specified" or "marked" and that the syntactic structure of the subject plays a role in checking features. It is argued here that the structure intervening between the subject and verb also plays a role in checking and that there is pressure to check features immediately. A self-paced reading study tested this proposal in a previously unstudied configuration: agreement between the verb in a subject relative clause (RC) and the relative clause head (e.g., the niece of the actors who was/were...). According to the Construal Hypothesis (Frazier and Clifton, 1995), the structural relation between the RC and head is not immediately fully specified (unlike, for example, the relation between the subject and verb of a main clause). Thus, at the point when an agreeing verb is processed, the structure underlying the check may not yet be fully specified. This assumption about structural processing, together with the proposal for agreement checking in comprehension predicts (1) that there will be a large asymmetry between the processing of singular and plural agreeing verbs in the RC (larger than those seen in direct subject-verb predication) and (2) that there could be a role for agreement in determining RC attachment. Clear evidence for the first prediction was found: evidence for the second was inconclusive.

Principles and practice of unification factoring

The efficiency of resolution-based logic programming languages, such as Prolog, depends critically on selecting and executing sets of applicable clause heads to resolve against subgoals. Traditional approaches to this problem have focused on using indexing to determine the smallest possible applicable set. Despite their usefulness, these approaches ignore the nondeterminism inherent in many programming languages to the extent that they do not attempt to optimize execution after the applicable set has been determined. Unification factoring seeks to rectify this omission by regarding the indexing and unification phases of clause resolution as a single process. This article formalizes that process through the construction of factoring automata . A polynomial-time algorithm is given for constructing optimal factoring automata that preserve the clause selection strategy of Prolog. More generally, when the clause selection strategy is not fixed, constructing such an optimal automaton is shown to be NP-complete, solving an open trie minimization problem. Unification factoring is implemented through a source code transformation that preserves the full semantics of Prolog. This transformation is specified in the article, and using it, several well-known programs show significant performance improvements across several different systems. A prototype of unification factoring is available by anonymous ftp.