Head-driven phrase structure grammar (HPSG) is one of the most prominent theories employed in deep parsing of natural language. Many linguistic theories are arguably best formalized in extensions of modal or dynamic logic (Keller, Feature logics, infinitary descriptions and grammar, 1993; Kracht, Linguistics Philos 18:401–458, 1995; Moss and Tiede, In: Blackburn, van Benthem, and Wolther (eds.) Handbook of modal logic, 2006), and HPSG seems to be no exception. Adequate extensions of dynamic logic have not been studied in detail, (...) however; the most important aspect is the reference to sets of substructures. In this paper, an adequate extension is identified, and some important results are established: Satisfiability is highly undecidable, and model checking is shown to be in EXPTIME and PSPACE-hard. A fragment with polynomial time model checking procedures is identified; it is shown to cover considerable fragments of HPSG. (shrink)

The SRL of King is a sound, complete and decidable logic designed specifically to support formalisms for the HPSG of Pollard and Sag. The SRL notion of modellability in a signature is particularly important for HPSG, and the present paper modifies an elegant method due to Blackburn and Spaan in order to prove that – modellability in each computable signature is 1 0 – modellability in some finite signature is 1 0 -hard, and – modellability in some (...) finite signature is decidable. (shrink)

This chapter focuses on the frameworks of Head‐Driven Phrase Structure Grammar (HPSG) as it developed from Generalized Phrase Structure Grammar (GPSG), and Lexical‐Functional Grammar (LFG). Declarative frameworks are not generative, as they do not ‘generate’ anything in the sense of the preceding paragraph. Pullum refers to that kind of approach as Generative‐Enumerative Syntax and differentiates it from Model‐Theoretic Syntax: GPSG, HPSG, and LFG essentially fall in the latter category. It describes some key aspects of declarative frameworks, and the (...) motivation for them. The chapter considers how declarative frameworks instantiate a view of Generative Grammar directly inspired by Noam Chomsky's early work, but without the procedural component. It presents some of the core design features which motivate declarative frameworks, and explores how syntactic phenomena are factorized and formalized in declarative frameworks, with a view to comparison with Minimalist Program analyses. (shrink)

The paper presents a system for construction classification representing multiple levels of specification, such as grammatical functions, grammatically reflected actants, and lexical semantics, aligned with a compositional system of sign combination mediating between a construction perspective and a valence perspective. The system uses a feature structure formalism based on Head-Driven Phrase Structure Grammar but with essential elements from Lexical Functional Grammar, and has as implementation background large scale HPSG grammars. While on the one extreme being able to encode word (...) level selection in multi-word patterns, the system on the other provides a compact format for construction specification, allowing for cross-language comparison both in construction and valence frame inventories. Pivotal in these capacities as well as in sign formalization in general are the grammatical functions. The paper motivates the usefulness of the various functionalities and illustrates the way in which they work together in a formally uniform system. (shrink)

Explication is the conceptual cornerstone of Carnap’s approach to the methodology of scientific analysis. From a philosophical point of view, it gives rise to a number of questions that need to be addressed, but which do not seem to have been fully addressed by Carnap himself. This paper reconsiders Carnapian explication by comparing it to a different approach: the ‘formalisms as cognitive tools’ conception. The comparison allows us to discuss a number of aspects of the Carnapian methodology, as well (...) as issues pertaining to formalization in general. We start by introducing Carnap’s conception of explication, arguing that there is a tension between his proposed criteria of fruitfulness and similarity; we also argue that his further desideratum of exactness is less crucial than might appear at first. We then bring in the general idea of formalisms as cognitive tools, mainly by discussing the reliability of so-called statistical prediction rules, i.e. simple algorithms used to make predictions across a range of areas. SPRs allow for a concrete instantiation of Carnap’s fruitfulness desideratum, which is arguably the most important desideratum for him. Finally, we elaborate on what we call the ‘paradox of adequate formalization’, which for the Carnapian corresponds to the tension between similarity and fruitfulness. We conclude by noting that formalization is an inherently paradoxical enterprise in general, but one worth engaging in given the ‘cognitive boost’ it affords as a tool for discovery. (shrink)

We consider the use ofevolving algebra methods of specifying grammars for natural languages. We are especially interested in distributed evolving algebras. We provide the motivation for doing this, and we give a reconstruction of some classic grammar formalisms in directly dynamic terms. Finally, we consider some technical questions arising from the use of direct dynamism in grammar formalisms.

This article explores the relation between the concept of symmetry and its formalisms. The standard view among philosophers and physicists is that symmetry is completely formalized by mathematical groups. For some mathematicians however, the groupoid is a competing and more general formalism. An analysis of symmetry that justifies this extension has not been adequately spelled out. After a brief explication of how groups, equivalence, and symmetries classes are related, we show that, while it’s true in some instances that groups (...) are too restrictive, there are other instances for which the standard extension to groupoids is too un restrictive. The connection between groups and equivalence classes, when generalized to groupoids, suggests a middle ground between the two. *Received July 2007. †To contact the authors, please write to: Alexandre Guay, UFR Sciences et Techniques, Université de Bourgogne, 9 Avenue Alain Savary, 21078 Dijon Cedex, France; e‐mail: [email protected] ; or to Brian Hepburn, Department of Philosophy, University of British Columbia, 1866 Main Mall E370, Vancouver, BC, Canada V6T 1Z1; e‐mail: [email protected]. (shrink)

Scientific models need to be investigated if they are to provide valuable information about the systems they represent. Surprisingly, the epistemological question of what enables this investigation has hardly been investigated. Even authors who consider the inferential role of models as central, like Hughes or Bueno and Colyvan, content themselves with claiming that models contain mathematical resources that provide inferential power. We claim that these notions require further analysis and argue that mathematical formalisms contribute to this inferential role. We (...) characterize formalisms, illustrate how they extend our mathematical resources, and highlight how distinct formalisms offer various inferential affordances. (shrink)

Familiar proof theoretical and especially automated deduction methods sometimes accept infinity where, in fact, it can be omitted. Our first example deals with the infinite supply of individual variables admitted in 1-order deductions, the second one deals with infinite-branching rules in sequent calculi with number-theoretical induction. The contents of Section 1 summarize and extend basic ideas and results published elsewhere, whereas basic ideas and results of Section 2 are exposed for the first time in the present paper. We consider classical (...) formalisms only, to which constructive formalisms can be reduced by Shanin-style interpretations. (shrink)

We present a rendering of some common grammatical formalisms in terms of evolving algebras. Though our main concern in this paper is on constraint-based formalisms, we also discuss the more basic case of context-free grammars. Our aim throughout is to highlight the use of evolving algebras as a specification tool to obtain grammar formalisms.

I will try to do three things in this paper. First, I want to situate certain problems in natural language semantics with respect to larger trends in logicism, including: (i) Attempts by positivist philosophers earlier in this century to provide a logical basis for the physical sciences; (ii) Attempts by linguists and logicians to develop a “natural language ontology” (and, presumably, a logical language that is related to this ontology by formally explicit rules) that would serve as a framework for (...) natural language semantics. (shrink)

Sequent calculi constitute an interesting and important category of proof systems. They are much less known than axiomatic systems or natural deduction systems are, and they are much less known than they should be. Sequent calculi were designed as a theoretical framework for investigations of logical consequence, and they live up to the expectations completely as an abundant source of meta-logical results. The goal of this book is to provide a fairly comprehensive view of sequent calculi -- including a wide (...) range of variations. The focus is on sequent calculi for various non-classical logics, from intuitionistic logic to relevance logic, through linear and modal logics. A particular version of sequent calculi, the so-called consecution calculi, have seen important new developments in the last decade or so. The invention of new consecution calculi for various relevance logics allowed the last major open problem in the area of relevance logic to be solved positively: pure ticket entailment is decidable. An exposition of this result is included in chapter 9 together with further new decidability results (for less famous systems). A series of other results that were obtained by J. M. Dunn and me, or by me in the last decade or so, are also presented in various places in the book. Some of these results are slightly improved in their current presentation. Obviously, many calculi and several important theorems are not new. They are included here to ensure the completeness of the picture; their original formulations may be found in the referenced publications. This book contains very little about semantics, in general, and about the semantics of non-classical logic in particular. (shrink)

The often observed complexity gap between the expressiveness of a logical formalism and its exponentially harder expression complexity is proven for all logical formalisms which satisfy natural closure conditions. The expression complexity of the prefix classes of second-order logic can thus be located in the corresponding classes of the weak exponential hierarchies; further results about expression complexity in database theory, logic programming, nonmonotonic reasoning, first-order logic with Henkin quantifiers and default logic are concluded. The proof method illustrates the significance (...) of quantifier-free interpretations in descriptive complexity theory. (shrink)

We show how to encode context-free string grammars, linear context-free tree grammars, and linear context-free rewriting systems as Abstract Categorial Grammars. These three encodings share the same constructs, the only difference being the interpretation of the composition of the production rules. It is interpreted as a first-order operation in the case of context-free string grammars, as a second-order operation in the case of linear context-free tree grammars, and as a third-order operation in the case of linear context-free rewriting systems. This (...) suggest the possibility of defining an Abstract Categorial Hierarchy. (shrink)

To study the interaction of forces that produce chest wall motion, we propose a model based on the lever system of Hillman and Finucane :951–961, 1987) and introduce some dynamic properties of the respiratory system. The passive elements are considered as elastic compartments linked to the open air via a resistive tube, an image of airways. The respiratory muscles force is applied to both compartments. Parameters of the model are identified in using experimental data of airflow signal measured by pneumotachography (...) and rib cage and abdomen signals measured by respiratory inductive plethysmography on eleven healthy volunteers in five conditions: at rest and with four level of added loads. A breath by breath analysis showed, whatever the individual and the condition are, that there are several breaths on which the airflow simulated by our model is well fitted to the airflow measured by pneumotachography as estimated by a determination coefficient R2 ≥ 0.70. This very simple model may well represent the behaviour of the chest wall and thus may be useful to interpret the relative motion of rib cage and abdomen during quiet breathing. (shrink)

Starting from a unitary, Lorentz invariant two-particle scattering amplitude, we show how to use an identification and replacement process to construct a unique, unitary particle–antiparticle amplitude. This process differs from conventional on-shell Mandelstam s, t, u crossing in that the input and constructed amplitudes can be off-diagonal and off-energy shell. Further, amplitudes are constructed using the invariant parameters which are appropriate to use as driving terms in the multi-particle, multichannel non-perturbative, cluster decomposable, relativistic scattering equations of the Faddeev-type integral equations (...) recently presented by Alfred, Kwizera, Lindesay and Noyes. It is therefore anticipated that when so employed, the resulting multi-channel solutions will also be unitary. The process preserves the usual particle–antiparticle symmetries. To illustrate this process, we construct a J=0 scattering length model chosen for simplicity. We also exhibit a class of physical models which contain a finite quantum mass parameter and are Lorentz invariant. These are constructed to reduce in the appropriate limits, and with the proper choice of value and sign of the interaction parameter, to the asymptotic solution of the non-relativistic Coulomb problem, including the forward scattering singularity, the essential singularity in the phase, and the Bohr bound-state spectrum. (shrink)

The classical limit problem refers to how the classical or Newtonian dynamics can be recovered from the principles of quantum mechanics. In other words the problem is how to reduce classical physics to quantum theory. It is commonplace to find in popular quantum mechanics texts that the problem is solved, nevertheless here we present a critique of these supposed solutions to the problem and we show why they are not really satisfactory. What we propose is to approach the problem from (...) the alternative theories to the standard quantum formalism; in particular from the pilot-wave theory and also GRW (with mass density). Both theories are better equipped to deal with the classical limit problem because they have a clear and precise ontology, which makes it easier to link their theoretical elements to the world of experience. This notwithstanding, there still remain some obstacles to overcome for said theories and here we propose how a general solution to this should look like. (shrink)

Recent attention to "self-consistent" (Rosser-style) systems raises anew the question of the proper interpretation of the Gödel Second Incompleteness Theorem and its effect on Hilbert's Program. The traditional rendering and consequence is defended with new arguments justifying the intensional correctness of the derivability conditions.

We show how to encode context-free string grammars, linear context-free tree grammars, and linear context-free rewriting systems as Abstract Categorial Grammars. These three encodings share the same constructs, the only difference being the interpretation of the composition of the production rules. It is interpreted as a first-order operation in the case of context-free string grammars, as a second-order operation in the case of linear context-free tree grammars, and as a third-order operation in the case of linear context-free rewriting systems. This (...) suggest the possibility of defining an Abstract Categorial Hierarchy. (shrink)

The broader context for the formal darwinism project established by two of the commentators, in terms of reconciling the Modern Synthesis with Darwinian arguments over design and in terms of links to other types of selection and design, is discussed and welcomed. Some overselling of the project is admitted, in particular of whether it claims to consider all organic design. One important fundamental question raised in two commentaries is flagged but not answered of whether design is rightly represented by an (...) optimisation program, and another from one commentary of whether the coreplicon dissolves in the face of multi-generational imprinting. Calls for the project to be extended to design at levels above and below the individual are considered sympathetically, but judged impractical at the high level of abstraction of the project. All claims of substantive technical error are emphatically rejected. Close technical readings are welcomed that, among other things, represent the project as 'axiomatizing fitness'. The prospects for the project are set out in the light of this highly varied set of commentaries. (shrink)

We show that Kubota and Levine’s characterization of the HPSG-based theory of non-constituent coordination proposed in Yatabe Proceedings of the 7th International Conference on Head-Driven Phrase Structure Grammar, CSLI, Stanford, pp 325–344, 2001) and later works is inaccurate, and that the theory in question does not require any ad hoc mechanisms to account for the long-known fact that right-node raising and left-node raising can affect semantic interpretation. In the course of demonstrating this, we fill in some details of this (...) HPSG-based theory that were left unspecified in the previous literature, and we also present novel accounts of split-antecedent relative clauses and of respectively interpretation that are consistent with the theory. Furthermore, we argue that the phenomenon of summative agreement may provide a reason to prefer this theory over CG-based theories like Kubota and Levine’s. (shrink)

Integrated Information Theory (IIT) stands out as one of the most promising theories for dealing with the hard problem of consciousness. Founded on five axioms derived from phenomenology, IIT seeks for the physical substrate of consciousness that complies with such axioms according to the criterion of maximally integrated information (Φ). Eventually, IIT identifies phenomenal consciousness with maximal Φ or, what is the same thing, with the strongest cause-effect power in the system. Among the scholars critical of this theory, some point (...) to the so-called Intrinsicality Problem (IP), namely that consciousness cannot be an intrinsic property of the system because maximal Φ crucially depends on the possible existence of bigger values of Φ if the initial system is appropriately linked to or embedded in larger systems. Although proposals in the recent literature aim to solve the IP by going beyond reductionism and physicalism, none of them tackle the real issue, i.e., the insufficiency of IIT’s causal-metaphysical structure. This papers endeavors to provide a solution to the IP in IIT within a hylomorphist ontology that includes formal causation. Complementing IIT with formal causation provides the theory with a criterion of individuation that solves the IP and, by relaxing identification between maximal Φ and consciousness, it lends a more robust metaphysical structure. To wit, maximal Φ is a necessary but not sufficient condition for the existence of consciousness. (shrink)

Formal languages are widely regarded as being above all mathematical objects and as producing a greater level of precision and technical complexity in logical investigations because of this. Yet defining formal languages exclusively in this way offers only a partial and limited explanation of the impact which their use actually has. In this book, Catarina Dutilh Novaes adopts a much wider conception of formal languages so as to investigate more broadly what exactly is going on when theorists put these tools (...) to use. She looks at the history and philosophy of formal languages and focuses on the cognitive impact of formal languages on human reasoning, drawing on their historical development, psychology, cognitive science and philosophy. Her wide-ranging study will be valuable for both students and researchers in philosophy, logic, psychology and cognitive and computer science. (shrink)

This paper presents a formalization of informal logic using the Carneades Argumentation System, a formal, computational model of argument that consists of a formal model of argument graphs and audiences. Conflicts between pro and con arguments are resolved using proof standards, such as preponderance of the evidence. CAS also formalizes argumentation schemes. Schemes can be used to check whether a given argument instantiates the types of argument deemed normatively appropriate for the type of dialogue.

Extant research underlines the critical challenge for firms to rigorously and consistently evaluate their growing number of cross-sector partnerships for sustainability and suggests formalizing evaluation processes by introducing formal practices. However, empirical research is scant and inconclusive. This study aims to develop an empirically grounded understanding of how firms formalize the evaluation processes of such partnerships and of what drives this formalization, to complement the so far mostly conceptual literature. We inductively analyzed 31 semi-structured interviews with 33 experts from firms (...) and their partnering nonprofits and further secondary data on organizations’ partnerships. We contribute to the cross-sector partnership research by analyzing firms’ practices related to the formalization of the internal as well as the joint partnership evaluation process with nonprofits. We propose a conceptual framework to explain why firms implement different formal practices to reduce the dependency on individuals’ skills, experiences, or judgments in evaluating partnerships. (shrink)

Formal ontology combines two ideas, one originating with Husserl, the other with Frege: that of ontology of the formal aspects of all objects, irrespective of their particular nature, and ontology pursued by employing the tools of modern formal disciplines, notably logic and semantics. These two traditions have converged in recent years and this is the first collection to encompass them as a whole in a single volume. It assembles essays from authors around the world already widely known for their work (...) in formal ontology, and illustrates that through the application of formal methods the ancient discipline of ontology may be put on a firm methodological basis. The essays not only illuminate the nature of ontology and its relation to other areas, in language, logic and everyday life, but also demonstrate that common issues from the analytical and phenomenological traditions may be discussed without ideological barriers. Audience: advanced students of and specialists in philosophy, linguistics, cognitive science, computer science, database engineering. (shrink)