Hybrid-Dynamic Ehrenfeucht-Fraïssé Games

This paper shows how to increase the expressivity of concept languages using a strategy called hybridization. Building on the welldknown correspondences between modal and description logics, two hybrid languages are defined. These languages are called ‘hybrid’ because, as well as the familiar propositional variables and modal operators, they also contain variables across individuals and a binder that binds these variables. As is shown, combining aspects of modal and firstdorder logic in this manner allows the expressivity of concept languages to be boosted in a natural way, making it possible to define number restrictions, collections of individuals, irreflexivity of roles, and TBoxd and ABoxdstatements. Subsequent addition of the universal modality allows the notion of subsumption to be internalized, and enables the representation of queries to arbitrary firstdorder knowledge bases. The paper notes themes shared by the hybrid and concept language literatures, and draws attention to a littledknown body of work by the late Arthur Prior.

An architecture for hybrid language systems is presented. A hybrid language has features of both textual languages and visual languages. Textual languages are computer-oriented and are geared toward storage, syntax analysis, and editing. On the other hand, visual languages are human-oriented and are geared toward expressive power, understandability, direct manipulation, and learning cost. Although a hybrid language system has the advantages of both textual and visual languages, general architectures to develop the corresponding programming environment considering real-time processing, synchronization, and multiple platforms have not yet been proposed. In the present paper, an architecture for hybrid language systems that support the development of new hybrid languages and the corresponding programming environments is presented. Implementation methods based on this architecture is demonstrated, and a case study is presented.

The article deals with the peculiarities of linguistic and cultural changes of language structure influenced by globalization process within the language contacts’ interaction. The analysis of various aspects in the modern society proves the dominance of the English language in the formation of the world collaboration. According to the research, English hybrid languages or new Englishes, based on the Standard English norms, are forced to adapt to the local linguistic and cultural needs. These hybrid languages perform the mixture of indigenous languages’ structure and Standard English rules, thought in many cases English dominates and replaces phonetic, lexical, syntactic elements of indigenous languages. Much attention in the work is paid to the peculiarities of such hybrid language as Nigerian English, which presents the local language variant, functioning in Nigeria. Owing to language contacts’ cooperation, Nigerian English combines the language features of Standard English rules and Nigerian local languages’ peculiarities.

In this paper we present a translation principle, called the axiomatic translation , for reducing propositional modal logics with background theories, including triangular properties such as transitivity, Euclideanness and functionality, to decidable fragments of first-order logic. The goal of the axiomatic translation principle is to find simplified theories, which capture the inference problems in the original theory, but in a way that can be readily automated and is easier to deal with by existing (first-order) theorem provers than the standard translation. The principle of the axiomatic translation is conceptually very simple and can be almost completely automated. Soundness is automatic under reasonable assumptions, general decidability results can be stated and termination of ordered resolution is easily achieved. The non-trivial part of the approach is proving completeness. We prove results of completeness, decidability, model generation, the small model property and the interpolation property for a number of common and less common modal logics. We also present results of experiments with a number of first-order logic theorem provers which are very encouraging.

In the study of modal and nonclassical logics, translations have frequently been employed as a way of measuring the inferential capabilities of a logic. It is sometimes claimed that two logics are “notational variants” if they are translationally equivalent. However, we will show that this cannot be quite right, since first-order logic and propositional logic are translationally equivalent. Others have claimed that for two logics to be notational variants, they must at least be compositionally intertranslatable. The definition of compositionality these accounts use, however, is too strong, as the standard translation from modal logic to first-order logic is not compositional in this sense. In light of this, we will explore a weaker version of this notion that we will call schematicity and show that there is no schematic translation either from first-order logic to propositional logic or from intuitionistic logic to classical logic.

Forgetting is an operation on knowledge bases that has been addressed in different areas of Knowledge Representation and with respect to different formalisms, including classical propositional and first-order logic, modal logics, logic programming, and description logics. Definitions of forgetting have been expressed in terms of manipulation of formulas, sets of postulates, isomorphisms between models, bisimulations, second-order quantification, elementary equivalence, and others. In this paper, forgetting is regarded as an abstract belief change operator, independent of the underlying logic. The central thesis is that forgetting amounts to a reduction in the language, specifically the signature, of a logic. The main definition is simple: the result of forgetting a portion of a signature in a theory is given by the set of logical consequences of this theory over the reduced language. This definition offers several advantages. Foremost, it provides a uniform approach to forgetting, with a definition that is applicable to any logic with a well-defined consequence relation. Hence it generalises a disparate set of logic-specific definitions with a general, high-level definition. Results obtained in this approach are thus applicable to all subsumed formal systems, and many results are obtained much more straightforwardly. This view also leads to insights with respect to specific logics: for example, forgetting in first-order logic is somewhat different from the accepted approach. Moreover, the approach clarifies the relation between forgetting and related operations, including belief contraction.

Current (heterogeneous) multi-core environments such as GPU architectures are hard to program with normal imperative and object-oriented (OO) languages because of race-conditions and general side-effects that code may have. We propose that both problems can be solved with a hybrid language that combines both Functional Programming (FP) and OO programming. By auto-parallelization in the FP-core, all loops and non-dependent calls can be executed in parallel. FP is to be used to write computationally intensive code with safe concurrent memory access. OO is to be used for I/O and management related tasks. In this article, we propose a new clean way to integrate the two language cores that even grants some restricted means to read and write arrays and objects from within FP mode. For the proposed new language features we have developed a compiler prototype that transparently parallelizes code to target both Cuda and multi-core machines (without annotations from the programmer) and that obtains good speedups.

Hybrid languages are modal languages that allow direct reference to the elements of a model. Even the basic hybrid language \( {\text{(}}\mathcal{H}{\text{(@))}} \), which only extends the basic modal language with the addition of nominals (i,j, k,...) and satisfiability operators (@ i , @ j , @ k ,...), increases the expressive power: it can explicitly check whether the point of evaluation is a specific, named point in the model (w ⊩ i), and whether a named point satisfies a given formula (w ⊩ @ iϕ ). The extended expressivity allows one to define elegant decision algorithms, where nominals and @ play the role of labels, or prefixes, which are usually needed during the construction of proofs in the modal setup [5,3]. Note that they do so inside the object language. All these features we get with no increase in complexity: the complexity of the satisfiability problem for \( \mathcal{H}{\text{(@)}} \) is the same as for the basic modal language, PSPACE [2]. When we move to very expressive hybrid languages containing binders, we obtain an impressive boost in expressivity, but usually we also move beyond the boundaries of decidability. Classical binders like ∀ and ∃ (together with @) make the logic as expressive as first-order logic (FOL) while adding the more “modal” binder ↓ gives a logic weaker than FOL [1]. We refer to the Hybrid Logic site at http://www.hylo.net for a broad on-line bibliography.KeywordsObject LanguageDescription LogicDirect ResolutionModal LanguageHybrid LogicThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Ehrenfeucht-Fraisse games have been introduced as a means of characterizing the relation of elementary equivalence between structures, or relational database instances in first order logic (FO), or equivalently Relational Calculus. In∼the usual Ehrenfeucht-Fraisse games the rules are determined by a linear ordering of a fixed lenght or, equivalently, by a special kind of tree - a chain of a fixed length -, where each point of that ordering or node of that tree corresponds to a quantification operation. Here we consider Ehrenfeucht-Fraisse games whose rules are determined by arbitrary trees such that their nodes correspond either to quantification operations (“q-nodes”) or to connective operations (“c-nodes”). By playing games on trees, we can refine the class of sentences which are considered in a given game, since a tree represents a particular class of sentences. We define and study several variations of tree games, for first and second order logic (SO). We give a sufficient condition for FO and SO equivalence restricted to formulae with up to n connectives, and hence also a sufficient condition for the non expressibility of a given query in those logics with formulae whose number of logical connectives is less than a given integer. We also give a sufficient condition to prove simultaneous lower bounds in both the number of connectives and in the quantifier types needed to express a given property in FO. If we consider only quantifier types, we get a characterization of the relation of preservation of sentences in the fragment of FO with the given set of quantifier types. We also study tree games for Σ n and Π n formulae. To illustrate the use of our games we use them to prove lower bounds in the connective size for several FO queries, like size of a database, size of a clique in a graph, size of a unary relation, transitive property in a graph, and degree of a node in a graph. Regarding SO, we prove lower bounds for quantifier rank for the parity query.Finally, we give a precise characterization of the logic whose elementary equivalence is characterized by a given tree game, as well as several equivalent characterizations of the existence of a winning strategy for Duplicator in the classical Ehrenfeucht-Fraisse game.

In this paper the problem of interpolation for the family of countable infinitary graded modal logics is considered. It is well known that interpolation fails in general for these logics and it is then natural to ask for a semantical characterization (stronger than entailment) of pairs of graded formulae having an interpolant. This is obtained using the notion of entailment along elementary equivalence. More precisely, we prove that if L is a graded modal logic then a pair (ø, ψ) of graded formulae in L have an interpolant in L if, and only if, ø entails ψ along elementary equivalence with respect to L. This characterization is obtained by adapting to graded modal logics the method of consistency property modulo bisimulation, which was previously used in Infinitary Logic and Infinitary Modal Logic. In the case of full Countable Infinitary Graded Modal Logic we improve this result and show that this logic enjoys Craig interpolation. This is done using a characterization of graded bisimulation between models via isomorphism of their unravellings.

Every day Italian TV viewers are exposed to a vast amount of heavily mediated audiovisual texts translated into their native language which contain a wide array of references to all the specific aspects and features of the source languages and cultures. Dubbese is the hybrid language used by the Italian dubbing industry to transpose both fictional and non-fictional foreign TV and cinema productions. This paper will illustrate the results of a large scale research project based upon a corpus of over 300 hours of dubbed TV programmes which set out to assess what Italian TV viewers perceive and understand of the culture-specific references contained in dubbed filmic products .

The central claim of Enoch Aboh’s book is that creoles combine features of different languages spoken by people involved in their genesis. In the case of Haitian French Creole and the Surinamese English creoles, the main substrate languages in the formative founding period are claimed to be the languages of the Gbe group, part of the Kwa branch of the Niger-Congo family. After a summary of the book, the claims are evaluated. The book is considered well written and an excellent piece of scholarship but unfortunately its central claims failed to convince this reader. Creoles are seen as a result of failed acquisition. It is shown in the article that Bantu speakers were more numerous than Gbe speakers, on the basis of historical, genetic and linguistic evidence. Still, Bantu languages are structurally quite different from the creoles, which can be taken for an argument that Gbe as well only had a minimal influence on the grammatical structures of the creoles. The analytic structures are argued in the article to be as diverse for creoles as they are for the Gbe languages. Some structures are found to be different in all three creoles and five varieties of Gbe.

This article studies a series of important issues concerning Spanglish as a hybrid language. It discusses why Spanglish has constituted a growing topic of interest ever since it first attracted the attention of specialists, be it from a linguistic, literary, or social-cultural perspective. The study also discusses the main challenges Spanglish is expected to be confronted with in the (near) future given that, more than ever, the identity of its speakers is at stake. A final part argues in favor of the maintenance of Spanglish as a unique form of bilingualism. By adopting a cognitive and functional viewpoint on language, it is shown that the analysis of Spanglish grammar offers insights into the main characteristics of human language, including basic principles such as iconicity, economy, creativity, and productivity.

In his review (Kaplan [1966]) of the article in which Kripke first proposed his relational semantics for modal logic, David Kaplan posed the question: which properties of a binary relation are expressible by formulas of propositional modal logic? A class of Kripke frames is said to be modal-axiomatic if it comprises exactly the frames on which every one of some set of formulas of propositional modal logic is valid. This work is addressed to the problem, suggested by Kaplan's question, of characterizing the modal-axiomatic classes of Kripke frames. In §i we obtain such a characterization, in terms of closure under certain constructions. In §2 we show that, in the case of classes closed under elementary equivalence, much simpler constructions suffice.

The Adventures of Huckleberry Finn was met with great controversy once it came out. In addition to being attacked morally, some of these languages in the novel are considered inferior and “trashy”. We cannot, however, completely reject it. African-American English (AAE) is the most spoken dialect in the novel, with many phonetic and grammatical variants compared to the standard English. This paper compares and analyses the translation techniques used in three Chinese translations while examining the characteristics of AAE in Huck Finn. The study found that Cheng Shi prefers to use “yuyin feibai” to translate AAE, Xu Ruzhi primarily uses modal particles to reflect the features of spoken language and Zhang Wanli uses standardized translation. This paper hopes to provide some inspiration for future retranslation of the book.