The papers collected in this volume exemplify some of the trends in current approaches to logic, language and computation. Written by authors with varied academic backgrounds, the contributions are intended for an interdisciplinary audience. The first part of this volume addresses issues relevant for multi-agent systems: reasoning with incomplete information, reasoning about knowledge and beliefs, and reasoning about games. Proofs as formal objects form the subject of Part II. Topics covered include: contributions on logical frameworks, linear logic, and different (...) approaches to formalized reasoning. Part III focuses on representations and formal methods in linguistic theory, addressing the areas of comparative and temporal expressions, modal subordination, and compositionality. (shrink)

We examined the role of fitness, commonly assumed without proof to be conferred by the mastery of language, in shaping the dynamics of language evolution. To that end, we introduced island migration (a concept borrowed from population genetics) into the shared lexicon model of communication (Nowak et al., 1999). The effect of fitness linear in language coherence was compared to a control condition of neutral drift. We found that in the neutral condition (no coherence-dependent fitness) even a (...) small migration rate – less than 1% – suffices for one language to become dominant, albeit after a long time. In comparison, when fitness-based selection is introduced, the subpopulations stabilize quite rapidly to form several distinct languages. Our findings support the notion that language confers increased fitness. The possibility that a shared language evolved as a result of neutral drift appears less likely, unless migration rates over evolutionary times were extremely small. (shrink)

The notion of language in e-Learning is still not very clear from a technical as well as semantic point of view. In the era of Information Technology, it is more and more important to unify the principles of language used and its semantic meaning to be more simple and precise when taking into consideration online educational courses. During the last years, e-Learning courses have begun to be popular around the world as during an internet era, we tend to (...) find consolidated information sources on internet rather than in traditional courses which require our physical presence. The crucial issue which makes an e- Learning course function is the language used to transmit all the information to the students in a clear and effective manner. For such language to be considered effective, it is necessary to adjust it to the general standards adopted in an international environment. The notion of a language used in e-Learning also faces some problems as it should be so concise as to be accessible for everybody regardless of gender, nationality, and intellectual level. It is hard to standardise its principles, thus over the years many scientists have tried to unify the top requirements a perfect e-Learning course should have. Nowadays, most of the population should stop considering e-Learning as an alternative form of education and focus on developing new models and structures for education and learning that fully exploit the opportunities of today’s digital revolution. With a laptop, a mobile device and Wi-Fi, you can manage your own e-Learning course, and take courses yourself, at any time and place, in any language. A typical model of an e-Learning course is based on guided self-study with a linear progression through modules consisting of recorded lectures, course literature, written assignments and multiple-choice self-tests. Technology has got an even better solution which consists of standardising the learning process and adopting it to a commonly known level of difficulty which might be expected when considering its use by an average person. (shrink)

Spanning the period between Wittgenstein's return to Cambridge in 1929 and the first version of Philosophical Investigations in 1936, Piotr Dehnel explores the middle stage in Ludwig Wittgenstein's philosophical development and identifies the major issues which engrossed him, including phenomenology, philosophy of mathematics and philosophy of language. Contrary to the dominant perspective, Dehnel argues that this period was intrinsically different from the early and late stages and should not be viewed as a mere transitional phase. The distinctiveness of Wittgenstein's (...) middle work can be seen in his philosophical thinking as it unfolds in a non-linear trajectory: thoughts do not follow upon each other, ideas do not appear sequentially one by one, and insights do not form a straight chain. Dehnel portrays the diffused and multifarious quality of Wittgenstein's middle thinking, enabling readers to form a more comprehensive view of his entire philosophy and acquire a better grasp of his conceptual trajectory, complete with the intricacies and challenges that it poses. (shrink)

Punctured languages are languages whose words are partial words in the sense that the letters at some positions are unknown. We investigate to which extent restoration of punctured languages is possible if the number of unknown positions or the proportion of unknown positions per word, respectively, is bounded, and we study their relationships for different boundings. The considered restoration classes coincide with similarity classes according to some kind of similarity for languages. Thus all results we can also formulate in the (...) language of similarity. We show some hierarchies of similarity classes for each class from the Chomsky hierarchy and prove the existence of linear languages which are not δ -similar to any regular language for any δ < ½. For δ ≥ ½ this is unknown but it could only be possible in the case of non-slender linear languages. (shrink)

Lautemann et al. (1995) gave a descriptive characterisation of the class of context-free languages, showing that a language is context-free iff it is definable as the set of words satisfying some sentence of a particular logic (fragment) over words. The present notes discuss how to specialise this result to the class of linear languages. Somewhat surprisingly, what would seem the most straightforward specialisation actually fails, due to the fact that linear grammars fail to admit a Greibach normal form. We (...) identify an alternative specialisation, based on an alternative characterisation of context-free languages, also noted by Lautemann et al. (1995). (shrink)

This paper is concerned with the kind of non-linear causation that lies behind the production and comprehension of speech in discourse, where multiple ‘input’ data typically act in concert towards a determinate output. To this end Whitehead's philosophy of Process - in particular his theory of ‘prehensions’ — is applied to the analysis of pragmatic implication and inference in a short literary excerpt, which involves the most complex kind of prehension, the `intuitive judgment'. This leads to a number of conclusions (...) concerning the way in which patterns of linguistic behaviour can be evoked out of mere potentiality by contextually embedded prehensions that constrain and modulate the expression of intended discourse acts. Some of these constraints are attributable to the nature of focal consciousness itself. An extension of the Whiteheadian notion of ‘subjective aim’ (usually understood to preside over a single ‘actual occasion’) will be necessitated, since in discourse this can clearly both be suspended and divided into subordinate sub-aims while the overall aim, still unfulfilled, is inherited from occasion to occasion. (shrink)

This paper investigates logical aspects of combining linear orders as semantics for modal and temporal logics, with modalities for possible paths, resulting in a variety of branching time logics over classes of trees. Here we adopt a unified approach to the Priorean, Peircean and Ockhamist semantics for branching time logics, by considering them all as fragments of the latter, obtained as combinations, in various degrees, of languages and semantics for linear time with a modality for possible paths. We then consider (...) a hierarchy of natural classes of trees and bundled trees arising from a given class of linear orders and show that in general they provide different semantics. We also discuss transfer of definability from linear orders to trees and introduce a uniform translation from Priorean to Peircean formulae which transfers definability of properties of linear orders to definability of properties of all paths in trees. (shrink)

This paper presents an approach to artificial intelligence planning based on linear temporal logic (LTL). A simple and easy-to-use planning language is described, Planning Domain Description Language with control Knowledge (PDDL-K), which allows one to specify a planning problem together with heuristic information that can be of help for both pruning the search space and finding better quality plans. The semantics of the language is given in terms of a translation into a set of LTL formulae. Planning (...) is then reduced to “executing” the LTL encoding, i.e. to model search in LTL. The feasibility of the approach has been successfully tested by means of the system Pdk, an implementation of the proposed method. (shrink)

This paper is concerned with the kind of non-linear causation that lies behind the production and comprehension of speech in discourse, where multiple input data typically act in concert towards a determinate output. To this end Whitehead's philosophy of Process - in particular his theory of prehensions — is applied to the analysis of pragmatic implication and inference in a short literary excerpt, which involves the most complex kind of prehension, the `intuitive judgment'. This leads to a number of conclusions (...) concerning the way in which patterns of linguistic behaviour can be evoked out of mere potentiality by contextually embedded prehensions that constrain and modulate the expression of intended discourse acts. Some of these constraints are attributable to the nature of focal consciousness itself. An extension of the Whiteheadian notion of subjective aim (usually understood to preside over a single actual occasion) will be necessitated, since in discourse this can clearly both be suspended and divided into subordinate sub-aims while the overall aim, still unfulfilled, is inherited from occasion to occasion. (shrink)

I present a semantics for the language of first-order additive-multiplicative linear logic, i.e. the language of classical first-order logic with two sorts of disjunction and conjunction. The semantics allows us to capture intuitions often associated with linear logic or constructivism such as sentences = games, SENTENCES = resources or sentences = problems, where “truth” means existence of an effective winning strategy.The paper introduces a decidable first-order logic ET in the above language and gives a proof of its (...) soundness and completeness with respect to this semantics. Allowing noneffective strategies in the latter is shown to lead to classical logic.The semantics presented here is very similar to Blass's game semantics. Although there is no straightforward reduction between the two corresponding notions of validity, my completeness proof can likely be adapted to the logic induced by Blass's semantics to show its decidability, which was the main problem left open in Blass's paper.The reader needs to be familiar with classical logic and arithmetic. (shrink)

Group size is a function of relative neocortical volume in nonhuman primates. Extrapolation from this regression equation yields a predicted group size for modern humans very similar to that of certain hunter-gatherer and traditional horticulturalist societies. Groups of similar size are also found in other large-scale forms of contemporary and historical society. Among primates, the cohesion of groups is maintained by social grooming; the time devoted to social grooming is linearly related to group size among the Old World monkeys and (...) apes. To maintain the stability of the large groups characteristic of humans by grooming alone would place intolerable demands on time budgets. It is suggested that (1) the evolution of large groups in the human lineage depended on the development of a more efficient method for time-sharing the processes of social bonding and that (2) language uniquely fulfills this requirement. Data on the size of conversational and other small interacting groups of humans are in line with the predictions for the relative efficiency of conversation compared to grooming as a bonding process. Analysis of a sample of human conversations shows that about 60% of time is spent gossiping about relationships and personal experiences. It is suggested that language evolved to allow individuals to learn about the behavioural characteristics of other group members more rapidly than is possible by direct observation alone. (shrink)

As adults age, their performance on many psychometric tests changes systematically, a finding that is widely taken to reveal that cognitive information-processing capacities decline across adulthood. Contrary to this, we suggest that older adults'; changing performance reflects memory search demands, which escalate as experience grows. A series of simulations show how the performance patterns observed across adulthood emerge naturally in learning models as they acquire knowledge. The simulations correctly identify greater variation in the cognitive performance of older adults, and successfully (...) predict that older adults will show greater sensitivity to fine-grained differences in the properties of test stimuli than younger adults. Our results indicate that older adults'; performance on cognitive tests reflects the predictable consequences of learning on information-processing, and not cognitive decline. We consider the implications of this for our scientific and cultural understanding of aging. (shrink)

Name der Zeitschrift: Journal of Ancient History Jahrgang: 5 Heft: 2 Seiten: 280-303.

Linguistic category learning has been shown to be highly sensitive to linear order, and depending on the task, differentially sensitive to the information provided by preceding category markers (premarkers, e.g., gendered articles) or succeeding category markers (postmarkers, e.g., gendered suffixes). Given that numerous systems for marking grammatical categories exist in natural languages, it follows that a better understanding of these findings can shed light on the factors underlying this diversity. In two discriminative learning simulations and an artificial language learning (...) experiment, we identify two factors that modulate linear order effects in linguistic category learning: category structure and the level of abstraction in a category hierarchy. Regarding category structure, we find that postmarking brings an advantage for learning category diagnostic stimulus dimensions, an effect not present when categories are non‐confusable. Regarding levels of abstraction, we find that premarking of super‐ordinate categories (e.g., noun class) facilitates learning of subordinate categories (e.g., nouns). We present detailed simulations using a plausible candidate mechanism for the observed effects, along with a comprehensive analysis of linear order effects within an expectation‐based account of learning. Our findings indicate that linguistic category learning is differentially guided by pre‐ and postmarking, and that the influence of each is modulated by the specific characteristics of a given category system. (shrink)

Linguistic category learning has been shown to be highly sensitive to linear order, and depending on the task, differentially sensitive to the information provided by preceding category markers (premarkers, e.g., gendered articles) or succeeding category markers (postmarkers, e.g., gendered suffixes). Given that numerous systems for marking grammatical categories exist in natural languages, it follows that a better understanding of these findings can shed light on the factors underlying this diversity. In two discriminative learning simulations and an artificial language learning (...) experiment, we identify two factors that modulate linear order effects in linguistic category learning: category structure and the level of abstraction in a category hierarchy. Regarding category structure, we find that postmarking brings an advantage for learning category diagnostic stimulus dimensions, an effect not present when categories are non‐confusable. Regarding levels of abstraction, we find that premarking of super‐ordinate categories (e.g., noun class) facilitates learning of subordinate categories (e.g., nouns). We present detailed simulations using a plausible candidate mechanism for the observed effects, along with a comprehensive analysis of linear order effects within an expectation‐based account of learning. Our findings indicate that linguistic category learning is differentially guided by pre‐ and postmarking, and that the influence of each is modulated by the specific characteristics of a given category system. (shrink)

The main result of this paper is a normalizing system of natural deduction for the full language of intuitionistic linear logic. No explicit weakening or contraction rules for -formulas are needed. By the systematic use of general elimination rules a correspondence between normal derivations and cut-free derivations in sequent calculus is obtained. Normalization and the subformula property for normal derivations follow through translation to sequent calculus and cut-elimination.

Tim van Gelder, following Brandom, Collins and others, uses the so‐called wide content of capacities which support social, norm governed activities, such as language, to argue for their anti‐natural, abstract, but socially instituted nature and thence for the failure of the entire traditional mind‐body discussion as ill‐posed. We argue that his former conclusion is wrong, that such properties are naturalisable, complicated organisational properties of the complexly organised, non‐linearly interactive systems that human beings are. This analysis also provides principled support, (...) but on other grounds, for van Gelder’s latter conclusion. We outline a new naturalist approach to the organisational capacities of such systems that is intended to ground their biological, cognitive and social characters. (shrink)

Linear arithmetics are extensions of Presburger arithmetic () by one or more unary functions, each intended as multiplication by a fixed element (scalar), and containing the full induction schemes for their respective languages. In this paper, we construct a model of the 2‐linear arithmetic (linear arithmetic with two scalars) in which an infinitely long initial segment of “Peano multiplication” on is ‐definable. This shows, in particular, that is not model complete in contrast to theories and that are known to satisfy (...) quantifier elimination up to disjunctions of primitive positive formulas. As an application, we show that, as a discretely ordered module over the discretely ordered ring generated by the two scalars, does not have the NIP, answering negatively a question of Chernikov and Hils. (shrink)

In recent years we have seen a dramatic shift, in several different areas of communication studies, from an information-theoretic to a dynamic systems paradigm. In an information processing system, communication, whether between cells, mammals, apes, or humans, is said to occur when one organism encodes information into a signal that is transmitted to another organism that decodes the signal. In a dynamic system, all of the elements are continuously interacting with and changing in respect to one another, and an aggregate (...) pattern emerges from this mutual co-action. Whereas the information-processing paradigm looks at communication as a linear, binary sequence of events, the dynamic systems paradigm looks at the relation between behaviors and how the whole configuration changes over time. One of the most dramatic examples of the significance of shifting from an information processing to a dynamic systems paradigm can be found in the debate over the interpretation of recent advances in ape language research (ALR). To some extent, many of the early ALR studies reinforced the stereotype that animal communication is functional and stimulus bound, precisely because they were based on an information-processing paradigm that promoted a static model of communicative development. But Savage-Rumbaugh's recent results with bonobos has introduced an entirely new dimension into this debate. Shifting the terms of the discussion from an information-processing to a dynamic systems paradigm not only highlights the striking differences between Savage-Rumbaugh's research and earlier ALR studies, but further, it sheds illuminating light on the factors that underpin the development of communication skills in great apes and humans, and the relationship between communicative development and the development of language. Key Words: apes; ape language research (ALR); brain development; co-regulation; communication; dynamic systems; language development; symbols. (shrink)

The equivalence of leaf languages of tree adjoining grammars and monadic linear context-free grammars was shown about a decade ago. This paper presents a proof of the strong equivalence of these grammar formalisms. Non-strict tree adjoining grammars and monadic linear context-free grammars define the same class of tree languages. We also present a logical characterisation of this tree language class showing that a tree language is a member of this class iff it is the two-dimensional yield of an (...) MSO-definable three-dimensional tree language. (shrink)

A large body of psycholinguistic research demonstrates that both language processing and language acquisition are sensitive to the distributions of linguistic constructions in usage. Here we investigate how statistical distributions at different linguistic levels – morphological and lexical, and phrasal – contribute to the ease with which morphosyntax is processed and produced by second language learners. We analyze Chinese ESL learners’ knowledge of four English inflectional morphemes: -ed, -ing, and third-person -s on verbs, and plural -s on (...) nouns. In Elicited Imitation Tasks, participants listened to length- and difficulty-matched sentences each containing one target morpheme and typed the whole sentence as accurately as they could after a short delay. Experiment 1 investigated lexical and morphemic levels, testing the hypotheses that a morpheme is expected to be more easily processed when it is highly available, and highly reliable. Thirty sentences were made for each morpheme, divided into three Availability-Reliability Distribution groups on the basis of corpus analysis in the Corpus of Contemporary American English : 10 target words high in availability, 10 high in reliability, and 10 low in both reliability and availability. Responses were scored on whether the target morpheme was accurately reproduced given the provision of the correct lemma. A generalized linear mixed-effects logit model revealed fixed effects of morpheme type, availability, and reliability on the accuracy of morpheme provision. There were no effects of lemma frequency. Experiment 2 successfully replicated these results and extended the investigation to explore phrasal formulaicity by manipulating the frequency of the four-word strings in which the morpheme was embedded. GLMMs replicated the effects of word-form availability and reliability and additionally revealed independent phrase-superiority effects where morphemes were better reproduced in contexts of higher string-frequency. Taken together, these findings demonstrate that morpheme acquisition reflects the distributional properties of learners’ experience and the mappings therein between lexis, morphology, phraseology, and semantics. These conclusions support an emergentist view of the statistical symbolic learning of morphology where language acquisition involves the satisfaction of competing constraints across multiple grain-sizes of units. (shrink)

We investigate the theories of linear algebra, which were originally defined to study the question of whether commutativity of matrix inverses has polysize Frege proofs. We give sentences separating quantified versions of these theories, and define a fragment in which we can interpret a weak theory V 1 of bounded arithmetic and carry out polynomial time reasoning about matrices - for example, we can formalize the Gaussian elimination algorithm. We show that, even if we restrict our language, proves the (...) commutativity of inverses. (shrink)

In _The Boundaries of Babel_, Andrea Moro tells the story of an encounter between two cultures: contemporary theoretical linguistics and the cognitive neurosciences. The study of language within a biological context has been ongoing for more than fifty years. The development of neuroimaging technology offers new opportunities to enrich the "biolinguistic perspective" and extend it beyond an abstract framework for inquiry. As a leading theoretical linguist in the generative tradition and also a cognitive scientist schooled in the new imaging (...) technology, Moro is uniquely equipped to explore this. Moro examines what he calls the "hidden" revolution in contemporary science: the discovery that the number of possible grammars is not infinite and that their number is biologically limited. This radical but little-discussed change in the way we look at language, he claims, will require us to rethink not just the fundamentals of linguistics and neurosciences but also our view of the human mind. Moro searches for neurobiological correlates of "the boundaries of Babel" -- the constraints on the apparent chaotic variation in human languages -- by using an original experimental design based on artificial languages. He offers a critical overview of some of the fundamental results from linguistics over the last fifty years, in particular regarding syntax, then uses these essential aspects of language to examine two neuroimaging experiments in which he took part. He describes the two neuroimaging techniques used, but makes it clear that techniques and machines do not provide interesting data without a sound theoretical framework. Finally, he discusses some speculative aspects of modern research in biolinguistics regarding the impact of the linear structure of linguistics expression on grammar, and more generally, some core aspects of language acquisition, genetics, and evolution. (shrink)

Ernest Gellner's final book, first published in 1998, is a synoptic interpretation of the thought of Wittgenstein and Malinowski.

In this paper we will discuss the first order multiplicative intuitionistic fragment of linear logic, MILL1, and its applications to linguistics. We give an embedding translation from formulas in the Lambek Calculus to formulas in MILL1 and show this translation is sound and complete. We then exploit the extra power of the first order fragment to give an account of a number of linguistic phenomena which have no satisfactory treatment in the Lambek Calculus.

BackgroundType-Token Ratio, given its relatively simple hand computation, is one of the few LSA measures calculated by clinicians in everyday practice. However, it has significant well-documented shortcomings; these include instability as a function of sample size, and absence of clear developmental profiles over early childhood. A variety of alternative measures of lexical diversity have been proposed; some, such as Number of Different Words/100 can also be computed by hand. However, others, such as Vocabulary Diversity and the Moving Average Type Token (...) Ratio rely on complex resampling algorithms that cannot be conducted by hand. To date, no large-scale study of all four measures has evaluated how well any capture typical developmental trends over early childhood, or whether any reliably distinguish typical from atypical profiles of expressive child language ability.Materials and MethodsWe conducted linear and non-linear regression analyses for TTR, NDW, VocD, and MATTR scores for samples taken from 946 corpora from typically developing preschool children, engaged in adult-child toy play, from the Child Language Data Exchange System. These were contrasted with 504 samples from children known to have delayed expressive language skills. We also conducted a separate sub-analysis which examined possible contextual effects of sampling environment on lexical diversity.ResultsOnly VocD showed significantly different mean scores between the typically -developing children and delayed developing children group. Using TTR would actually misdiagnose typical children and miss children with known language impairment. However, computation of VocD as a function of toy interactions was significant and emerges as a further caution in use of lexical diversity as a valid proxy index of children’s expressive vocabulary skill.DiscussionThis large scale statistical comparison of computer-implemented algorithms for expressive lexical profiles in young children with traditional, hand-calculated measures showed that only VocD met criteria for evidence-based use in LSA. However, VocD was impacted by sample elicitation context, suggesting that non-linguistic factors, such as engagement with elicitation props, contaminate estimates of spoken lexical skill in young children. Implications and suggested directions are discussed. (shrink)

C. Karp has shown that if α is an ordinal with ω α = α and A is a linear ordering with a smallest element, then α and $\alpha \bigotimes A$ are equivalent in L ∞ω up to quantifer rank α. This result can be expressed in terms of Ehrenfeucht-Fraïssé games where player ∀ has to make additional moves by choosing elements of a descending sequence in α. Our aim in this paper is to prove a similar result for Ehrenfeucht-Fraïssé (...) games of length ω 1 . One implication of such a result will be that a certain infinite quantifier language cannot say that a linear ordering has no descending ω 1 -sequences (when the alphabet contains only one binary relation symbol). Connected work is done by Hyttinen and Oikkonen in [H] and [O]. (shrink)

We present an overview of linear-time temporal logics with Presburger constraints whose models are sequences of tuples of integers. Such formal specification languages are well-designed to specify and verify systems that can be modelled with counter systems. The paper recalls the general framework of LTL over concrete domains and presents the main decidability and complexity results related to fragments of Presburger LTL. Related formalisms are also briefly presented.

A nonempty sequence T1,...,Tn of theories is tolerant, if there are consistent theories T 1 + ,..., T n + such that for each 1 i n, T i + is an extension of Ti in the same language and, if i n, T i + interprets T i+1 + . We consider a propositional language with the modality , the arity of which is not fixed, and axiomatically define in this language the decidable logics TOL and (...) TOL. It is shown that TOL (resp. TOL) yields exactly the schemata of PA-provable (resp. true) arithmetical sentences, if (A1,..., An) is understood as (a formalization of) PA+A1, ..., PA+An is tolerant. (shrink)

Any approach to the study of managerial situations undertaken without reflection on the underpinning philosophy is flawed because it limits our ability to question the validity of the knowledge claimed in the analysis. The paper considers this issue and presents a philosophical reflection on the use of a systems approach to the modelling of human enterprises. It draws on insights from systems thinking, cognitive science, autopoiesis, communication theory and non-linear dynamics. These are interpreted within the context of social systems as (...) networks of conversations that are generated in language. It is written to invite an exchange of ideas concerning the role of the generative dialogue. (shrink)

In _The Boundaries of Babel_, Andrea Moro tells the story of an encounter between two cultures: contemporary theoretical linguistics and the cognitive neurosciences. The study of language within a biological context has been ongoing for more than fifty years. The development of neuroimaging technology offers new opportunities to enrich the "biolinguistic perspective" and extend it beyond an abstract framework for inquiry. As a leading theoretical linguist in the generative tradition and also a cognitive scientist schooled in the new imaging (...) technology, Moro is uniquely equipped to explore this. Moro examines what he calls the "hidden" revolution in contemporary science: the discovery that the number of possible grammars is not infinite and that their number is biologically limited. This radical but little-discussed change in the way we look at language, he claims, will require us to rethink not just the fundamentals of linguistics and neurosciences but also our view of the human mind. Moro searches for neurobiological correlates of "the boundaries of Babel" -- the constraints on the apparent chaotic variation in human languages -- by using an original experimental design based on artificial languages. He offers a critical overview of some of the fundamental results from linguistics over the last fifty years, in particular regarding syntax, then uses these essential aspects of language to examine two neuroimaging experiments in which he took part. He describes the two neuroimaging techniques used, but makes it clear that techniques and machines do not provide interesting data without a sound theoretical framework. Finally, he discusses some speculative aspects of modern research in biolinguistics regarding the impact of the linear structure of linguistics expression on grammar, and more generally, some core aspects of language acquisition, genetics, and evolution. (shrink)

Revisions of the King James Version of 1611 continued into the 20th and 21st centuries as literal or word-for-word translations. This development corresponds with a new age in Bible translation that started in the second half of the 20th century, which involves at least six changes in the philosophy of Bible translation. Firstly, Bible translation is characterised by interconfessional cooperation. Secondly, the plain meaning intended in the incipient texts is made accessible to readers. Thirdly, new critical editions of the Hebrew (...) and Greek incipient texts on the basis of new discoveries of texts are utilised. Fourthly, there is the tendency to remove archaic language to make versions intelligible. Fifthly, there is a tendency to use gendered and inclusive language. Sixthly, the move is from print communication, which can be typified as typographic interpretive culture, to electronic or media communication, which can be typified as digital-media interpretive culture, where sound and visuality become prominent as a contextual supplement to words. In the analysis it will be determined which of these aspects are reflected in the Revised Standard Version and its revisions as part of the linear emergence of the Tyndale–King James Version tradition. However, unlike the King James Version, the Revised Standard Version and its revisions failed to achieve widespread approval from satisfied readers, thus opening the door to alternative revisions.Contribution: Instead of viewing the Revised Standard Version and its revisions as new and independent from the Tyndale–King James Version tradition, it is demonstrated that they are a linear continuation of the emergence of the pre-20th century translation complex within this tradition without replicating the success of the King James Version. (shrink)

We present a semantic study of a family of modal intuitionistic linear systems, providing various logics with both an algebraic semantics and a relational semantics, to obtain completeness results. We call modality a unary operator on formulas which satisfies only one rale (regularity), and we consider any subsetW of a list of axioms which defines the exponential of course of linear logic. We define an algebraic semantics by interpreting the modality as a unary operation on an IL-algebra. Then we introduce (...) a relational semantics based on pretopologies with an additional binary relationr between information states. The interpretation of is defined in a suitable way, which differs from the traditional one in classical modal logic. We prove that such models provide a complete semantics for our minimal modal system, as well as, by requiring the suitable conditions onr (in the spirit of correspondence theory), for any of its extensions axiomatized by any subsetW as above. We also prove an embedding theorem for modal IL-algebras into complete ones and, after introducing the notion of general frame, we apply it to obtain a duality between general frames and modal IL-algebras. (shrink)

We present the model construction technique called Linear Realizability. It consists in building a category of Partial Equivalence Relations over a Linear Combinatory Algebra. We illustrate how it can be used to provide models, which are fully complete for various typed λ-calculi. In particular, we focus on special Linear Combinatory Algebras of partial involutions, and we present PER models over them which are fully complete, inter alia, w.r.t. the following languages and theories: the fragment of System F consisting of ML-types, (...) the maximal theory on the simply typed λ-calculus with finitely many ground constants, and the maximal theory on an infinitary version of this latter calculus. (shrink)

We argue that the need for commentary in commonly used linear calculi of natural deduction is connected to the “deletion” of illocutionary expressions that express the role of propositions as reasons, assumptions, or inferred propositions. We first analyze the formalization of an informal proof in some common calculi which do not formalize natural language illocutionary expressions, and show that in these calculi the formalizations of the example proof rely on commentary devices that have no counterpart in the original proof. (...) We then present a linear natural deduction calculus that makes use of formal illocutionary expressions in such a way that unique readability for derivations is guaranteed – thus showing that formalizing illocutionary expressions can eliminate the need for commentary. (shrink)