We prove that $\textbf {K}5$ and some of its extensions that do not contain $\textbf {K}4$ are of unification type $1$.

The problem of unification in a normal modal logic $L$ can be defined as follows: given a formula $\varphi$, determine whether there exists a substitution $\sigma$ such that $\sigma $ is in $L$. In this paper, we prove that for several non-symmetric non-transitive modal logics, there exists unifiable formulas that possess no minimal complete set of unifiers.

The unification problem in a normal modal logic is to determine, given a formula.

It is already known that unifiable formulas in normal modal logic |$\textbf {K}+\square ^{2}\bot $| are either finitary or unitary and unifiable formulas in normal modal logic |$\textbf {Alt}_{1}+\square ^{2}\bot $| are unitary. In this paper, we prove that for all |$d{\geq }3$|⁠, unifiable formulas in normal modal logic |$\textbf {K}+\square ^{d}\bot $| are either finitary or unitary and unifiable formulas in normal modal logic |$\textbf {Alt}_{1}+\square ^{d}\bot $| are unitary.

In this paper subvarieties of pseudocomplemented distributive lattices are classified by their unification type. We determine the unification type of every particular unification problem in each subvariety of pseudocomplemented distributive lattices.

We propose related algorithms for unification and constraint simplification in }F’&, a refinement of the simply-typed A-calculus with subtypes and bounded intersection types. }F""’ is intended as the basis of a logical framework in order to achieve more succinct and declarative axiomatiza-.

We show that the variety of Heyting algebras has finitary unification type. We also show that the subvariety obtained by adding it De Morgan law is the biggest variety of Heyting algebras having unitary unification type. Proofs make essential use of suitable characterizations (both from the semantic and the syntactic side) of finitely presented projective algebras.

A method is described for inducing a type-logical grammar from a sample of bare sentence trees which are annotated by lambda terms, called term-labelled trees . Any type logic from a permitted class of multimodal logics may be specified for use with the procedure, which induces the lexicon of the grammar including the grammatical categories. A first stage of semantic bootstrapping is performed, which induces a general form lexicon from the sample of term-labelled trees using Fulop’s (J Log (...) Lang Inf 14(1):49–86, 2005) procedure. Next we present a two-stage procedure for performing distributional learning by unifying the lexical types that are initially discovered. The first structural unification algorithm in essence unifies the initial family of sets of types so that the resulting grammar will generate all term-labelled trees that follow the usage patterns evident from the learning sample. Further altering the lexical categories to generate a recursively extended language can be accomplished by a second unification. The combined unification algorithm is shown to yield a new type-logical lexicon that extends the learning sample to a possibly infinite (and possibly context-sensitive) language in a principled fashion. Finally, the complete learning strategy is analyzed from the perspective of algorithmic learning theory; the range of the procedure is shown to be a class of term-labelled tree languages which is finitely learnable from good examples (Lange et al in Algorithmic learning theory, Vol 872 of lecture notes in artificial intelligence, Springer, Berlin, pp 423–437), and so is identifiable in the limit as a corollary. (shrink)

We investigate finitarity of unification types in locally finite varieties of Heyting algebras, giving both positive and negative results. We make essential use of finite dualities within a conceptualization for E-unification theory 733–752) relying on the algebraic notion of a projective object.

We define an order independent version of default unification on typed feature structures. The operation is one where default information in a feature structure typed with a more specific type, will override default information in a feature structure typed with a more general type, where specificity is defined by the subtyping relation in the type hierarchy. The operation is also able to handle feature structures where reentrancies are default. We provide a formal semantics, prove order independence (...) and demonstrate the utility of this version of default unification in several linguistic applications. First, we show how it can be used to define multiple orthogonal default inheritance in the lexicon in a fully declarative fashion. Secondly, we show how default lexical specifications (introduced via default lexical inheritance) can be made to usefully persist beyond the lexicon and interact with syntagmatic rules. Finally, we outline how persistent default unification might underpin default feature propagation principles and a more restrictive and constraint-based approach to lexical rules. (shrink)

Epistemic logics are essential to the design of logical systems that capture elements of reasoning about knowledge. In this paper, we study the computability of unifiability and the unification types in several epistemic logics.

In this paper we study the admissible rules of intermediate logics. We establish some general results on extensions of models and sets of formulas. These general results are then employed to provide a basis for the admissible rules of the Gabbay–de Jongh logics and to show that these logics have finitary unification type.

This paper contains a proof-theoretic account of unification in transitive reflexive modal logics, which means that the reasoning is syntactic and uses as little semantics as possible. New proofs of theorems on unification types are presented and these results are extended to negationless fragments. In particular, a syntactic proof of Ghilardi’s result that $\mathsf {S4}$ has finitary unification is provided. In this approach the relation between classical valuations, projective unifiers, and admissible rules is clarified.

We prove that the unification type of Łukasiewicz logic and of its equivalent algebraic semantics, the variety of MV-algebras, is nullary. The proof rests upon Ghilardiʼs algebraic characterisation of unification types in terms of projective objects, recent progress by Cabrer and Mundici in the investigation of projective MV-algebras, the categorical duality between finitely presented MV-algebras and rational polyhedra, and, finally, a homotopy-theoretic argument that exploits lifts of continuous maps to the universal covering space of the circle. We (...) discuss the background to such diverse tools. In particular, we offer a detailed proof of the duality theorem for finitely presented MV-algebras and rational polyhedra—a fundamental result that, albeit known to specialists, seems to appear in print here for the first time. (shrink)

This article compares the moral significance of two types of immigration, that which is based on the unification of citizens and non-citizens and that which is based on the skilled labor needs of the receiving society. I assess the interests of both citizens and non-citizens affected by each of these types of inflows and argue that unification admissions should be given priority over skilled workers but states retain a qualified moral permission to incentivize skilled worker migration.

In the current literature on scientific explanation unification became unfashionable in favour of causal approaches. We want to bring unification back into the picture. In this paper we demonstrate that resemblance questions do occur in scientific practice and that they cannot be properly answered without unification. Our examples show that resemblance questions about particular facts demand what we call causal network unification, while resemblance questions about regularities require what we call mechanism unification. We clarify how (...) these types of unification relate to Philip Kitcher’s account, but also to causal and mechanistic accounts of explanation. (shrink)

We show that adding compatible operations to Heyting algebras and to commutative residuated lattices, both satisfying the Stone law ¬x ⋁ ¬¬x = 1, preserves filtering unification, that is, the property that for every two unifiers there is a unifier more general then both of them. Contrary to that, often adding new operations to algebras results in changing the unification type. To prove the results we apply the theorems of [9] on direct products of l-algebras and filtering (...) unification. We consider examples of frontal Heyting algebras, in particular Heyting algebras with the successor, γ and G operations as well as expansions of some commutative integral residuated lattices with successor operations. (shrink)

In this article I argue that there are two different types of understanding: the understanding we get from explanations, and the understanding we get from unification. This claim is defended by first showing that explanation and unification are not as closely related as has sometimes been thought. A critical appraisal of recent proposals for understanding without explanation leads us to discuss the example of a purely classificatory biology: it turns out that such a science can give us understanding (...) of the world through unification of the phenomena, even though it does not give us any explanations. The two types of understanding identified in this paper, while strictly separate, do have in common that both consist in seeing how the individual phenomena of the universe hang together. Explanations give us connections between the phenomena through the asymmetric, ‘vertical’ relation of determination; unifications give us connections through the symmetric, ‘horizontal’ relation of kinship. We then arrive at a general definition of understanding as knowledge of connections between the phenomena, and indicate that there might be more than two types of understanding. (shrink)

This dissertation starts with a concise overview of what philosophers of science have written about unification and its role in scientific explanation during the last 50 years to provide the reader with some background knowledge. In order to bring unification back into the picture, I have followed two strategies, resulting respectively in Parts I and II of this dissertation. In Part I the idea of unification is used to refine and enrich the dominant causalmechanist and causal-interventionist accounts (...) of scientific explanation. In this part of the dissertation I bracket the classical ideas about unification: deduction and derivation. I do grant, for the sake of argument, that explanations are causal and argue that unification is important from within this causalist perspective. In Part II I continue my strategy of digging into scientific practice to find cases of ontological unification. But here I distance myself from the dominant literature that all explanations must be causal. I will investigate whether explanatory unification is possible in non-causal explanations. Part III contains some further reflections and conclusions. I will formulate my primary results, and I will elaborate on their implications for thinking about unification and explanation. The different forms of ontological unification were quite diverse. This relates to the method I have used. Throughout this dissertation the types of unification that were discussed emerged from digging into scientific practice. This philosophy-of-science-practice approach steered me towards a pluralistic view on unification and on explanation. In this dissertation I do not try to develop a new model of explanation and compare it to existing models. The aim is to show that there are important types of explanatory practice which cannot be properly analyzed if we neglect unification as a desideratum for explanations. (shrink)

L.L. Maksimova and L. Esakia, V. Meskhi showed that the modal logic \ has exactly 5 pretabular extensions PM1–PM5. In this paper, we study the problem of unification for all given logics. We showed that PM2 and PM3 have finitary, and PM1, PM4, PM5 have unitary types of unification. Complete sets of unifiers in logics are described.

Pluralism with respect to the structure of explanations of facts is not uncommon. The pluralism which Salmon and others have defended is compatible with several positions about the exact re-lation between these two types of explanations. We distinguish four such positions, and argue in favour of one of them. We also compare our results with the views of some authors who have recently written on this subject.

Pluralism with respect to the structure of explanations of facts is not uncommon. Wesley Salmon, for instance, distinguished two types of explanation: causal explanations (which provide insight in the causes of the fact we want to explain) and unification explanations (which fit the explanandum into a unified world view). The pluralism which Salmon and others have defended is compatible with several positions about the exact relation between these two types of explanations. We distinguish four such positions, and argue in (...) favour of one of them. We also compare our results with the views of some authors who have recently written on this subject. (shrink)

This article is a commentary on Machery (2009) Doing without Concepts. Concepts are mental symbols that have semantic structure and processing structure. This approach (1) allows for different disciplines to converge on a common subject matter; (2) it promotes theoretical unification; and (3) it accommodates the varied processes that preoccupy Machery. It also avoids problems that go with his eliminativism, including the explanation of how fundamentally different types of concepts can be co-referential.

Sober has reconstructed the biological design argument in the framework of likelihoodism, purporting to demonstrate that it is defective for intrinsic reasons. We argue that Sober’s restriction on the introduction of auxiliary hypotheses is too restrictive, as it commits him to rejecting types of everyday reasoning that are clearly valid. Our account shows that the design argument fails, not because it is intrinsically untestable but because it clashes with the empirical evidence and fails to satisfy certain theoretical desiderata (in particular, (...) unification). Likewise, Sober’s critique of the arguments from imperfections and from evil against design is off the mark. (shrink)

Many different, seemingly mutually exclusive, theories of categorization have been proposed in recent years. The most notable theories have been those based on prototypes, exemplars, and causal models. This chapter provides “representation theorems” for each of these theories in the framework of probabilistic graphical models. More specifically, it shows for each of these psychological theories that the categorization judgments predicted and explained by the theory can be wholly captured using probabilistic graphical models. In other words, probabilistic graphical models provide a (...) lingua franca for these disparate categorization theories, and so we can quite directly compare the different types of theories. These formal results are used to explain a variety of surprising empirical results, and to propose several novel theories of categorization. (shrink)

To be usable in practice, interactive theorem provers need to provide convenient and efficient means of writing expressions, definitions, and proofs. This involves inferring information that is often left implicit in an ordinary mathematical text, and resolving ambiguities in mathematical expressions. We refer to the process of passing from a quasi-formal and partially-specified expression to a completely precise formal one as elaboration. We describe an elaboration algorithm for dependent type theory that has been implemented in the Lean theorem prover. (...) Lean’s elaborator supports higher-order unification, type class inference, ad hoc overloading, insertion of coercions, the use of tactics, and the computational reduction of terms. The interactions between these components are subtle and complex, and the elaboration algorithm has been carefully designed to balance efficiency and usability. We describe the central design goals, and the means by which they are achieved. (shrink)

Higher order unification is a way of combining information (or equivalently, solving equations) expressed as terms of a typed higher order logic. A suitably restricted form of the notion has been used as a simple and perspicuous basis for the resolution of the meaning of elliptical expressions and for the interpretation of some non-compositional types of comparative construction also involving ellipsis. This paper explores another area of application for this concept in the interpretation of sentences containing intonationally marked focus, (...) or various semantic constructs which are sensitive to focus.Similarities and differences between this approach, and theories using alternative semantics, structured meanings, or flexible categorial grammars, are described. The paper argues that the higher order unification approach offers descriptive advantages over these alternatives, as well as the practical advantage of being capable of fairly direct computational implementation. (shrink)

Cartesian closed categories (CCCs) have played and continue to play an important role in the study of the semantics of programming languages. An axiomatization of the isomorphisms which hold in all Cartesian closed categories discovered independently by Soloviev and Bruce, Di Cosmo and Longo leads to seven equalities. We show that the unification problem for this theory is undecidable, thus settling an open question. We also show that an important subcase, namely unification modulo the linear isomorphisms, is NP-complete. (...) Furthermore, the problem of matching in CCCs is NP-complete when the subject term is irreducible. CCC-matching and unification form the basis for an elegant and practical solution to the problem of retrieving functions from a library indexed by types investigated by Rittri. It also has potential applications to the problem of polymorphic type inference and polymorphic higher-order unification, which in turn is relevant to theorem proving and logic programming. (shrink)

In this paper the notion of unifier is extended to the infinite set case. The proof of existence of the most general unifier of any infinite, unifiable set of types (terms) is presented. Learning procedure, based on infinite set unification, is described.

In this chapter I discuss the attempts by Theodor Kaluza [Kaluza, T., 1921. Zum Unitätproblem der Physik. Sitzungsber. der K. Ak. der Wiss. zu Berlin, 966–972] and by Oskar Klein [Klein, O., 1926a. Quantentheorie und fünfdimensionale Relativitätstheorie. Zeitschrift für Physik 37 (12), 895–906; Klein, O., 1926b. The atomicity of electricity as a quantum theory law. Nature 118, 516], respectively, to unify electromagnetism and general relativity within a five-dimensional Riemannian manifold. I critically compare Kaluza's results to Klein's. Klein's theory possesses more (...) explanatory power and unificatory strength and uses less types of brute facts than Kaluza's. The characteristic feature of Klein's theory is that it relies on an extrinsic element of unification, i.e. the wavefunction behavior, which is not intrinsic to EM or GR. Finally, I compare and discuss Kaluza's and Klein's theories in the context of Tim Maudlin's [Maudlin, T., 1996. On the unification of physics. Journal of Philosophy 93 (3), 129–144] ranking of unification and I clarify in what sense they constitute counterexamples to some of Margaret Morrison's [Morrison, M., 2000. Unifying Scientific Theories: Physical Concepts and Mathematical Structures. Cambridge University Press] assertions about unification. (shrink)

We provide an algorithm for determining a categorial grammar from linguistic data that essentially uses unification of type-schemes assigned to atoms. The algorithm presented here extends an earlier one restricted to rigid categorial grammars, introduced in [4] and [5], by admitting non-rigid outputs. The key innovation is the notion of an optimal unifier, a natural generalization of that of a most general unifier.

Three types of unification patterns in the history of physics are considered. The paradigmatic example of synthesis is chosen to be Maxwell’s fusion of electricity, magnetism and light. The analysis of Maxwell’s works enables to extract three hallmarks of any successful scientific unification. The hallmarks appear to be crucial since any violation of them inevitably leads to a radical decrease of the unifying theory’s predictive power. It is contended that classical (Maxwell) and modern (Einstein) milestones of physics growth (...) are in good agreement with the rules extracted. However, all the three basic stages of ‘post-modern’ physics – i.e. the electroweak theory of Weinberg and Salam, GUTs and SUSY approach culminating in the superstrings – can be described as violations of the synthesis rules. (shrink)

John Polkinghorne claims there are no real distinctions between general providence, special providence and miracle. In this paper I determine whether this claim could be true given Polkinghorne’s wider account of these types of divine action. I conclude that this claim could be true, but only given a particular reading of Polkinghorne. I then defend this reading in light of two potential objections.

We construct the Extended Relativity Theory in Born-Clifford-Phase spaces with an upper R and lower length λ scales (infrared/ultraviolet cutoff). The invariance symmetry leads naturally to the real Clifford algebra Cl (2, 6, R) and complexified Clifford Cl C (4) algebra related to Twistors. A unified theory of all Noncommutative branes in Clifford-spaces is developed based on the Moyal-Yang star product deformation quantization whose deformation parameter involves the lower/upper scale $$(\hbar \lambda / R)$$. Previous work led us to show from (...) first principles why the observed value of the vacuum energy density (cosmological constant) is given by a geometric mean relationship $$\rho \sim L_{\rm Planck}^{-2}R^{-2} = L_{P}^{-4} (L_{\rm Planck} / R)^{2} \sim 10^{-122}M_{\rm Planck}^4$$, and can be obtained when the infrared scale R is set to be of the order of the present value of the Hubble radius. We proceed with an extensive review of Smith’s 8D model based on the Clifford algebra Cl (1, 7) that reproduces at low energies the physics of the Standard Model and Gravity, including the derivation of all the coupling constants, particle masses, mixing angles,....with high precision. Geometric actions are presented like the Clifford-Space extension of Maxwell’s Electrodynamics, and Brandt’s action related to the 8D spacetime tangent-bundle involving coordinates and velocities (Finsler geometries). Finally we outline the reasons why a Clifford-Space Geometric Unification of all forces is a very reasonable avenue to consider and propose an Einstein-Hilbert type action in Clifford-Phase spaces (associated with the 8D Phase space) as a Unified Field theory action candidate that should reproduce the physics of the Standard Model plus Gravity in the low energy limit. (shrink)

This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability. The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal language. This expressive notation (...) facilitates proofs of the classical incompleteness and undecidability theorems which are very elegant and easy to understand. The discussion of semantics makes clear the important distinction between standard and nonstandard models which is so important in understanding puzzling phenomena such as the incompleteness theorems and Skolem's Paradox about countable models of set theory. Some of the numerous exercises require giving formal proofs. A computer program called ETPS which is available from the web facilitates doing and checking such exercises. Audience: This volume will be of interest to mathematicians, computer scientists, and philosophers in universities, as well as to computer scientists in industry who wish to use higher-order logic for hardware and software specification and verification. (shrink)

This monograph introduces a meta-framework for conducting interdisciplinary research in the science of emotion, as well as a framework for a particular kind of theory of emotion. It can also be understood as a “cross-over” book that introduces neophytes to some of the current discourse and major challenges for an interdisciplinary approach to the science of emotion, especially from a philosophical perspective. It also engages experts from across the disciplines who are interested in conducting an interdisciplinary approach to research and (...) theorizing in the science of emotion, and introduces to them some of the contemporary debates in the philosophy of emotion. It does so by providing a taxonomy of theories of emotion which allows one to understand the contemporary interdisciplinary discourse in the science of emotion as a debate between four fundamental types of theories of emotion—realism, instrumentalism, eliminative-realism, and eliminativism—and which can be found or potentially found across the disciplines, and by arguing for foundational principles which can unify, without consilience, these four kinds of approaches as perspectives about the same object of inquiry. It also covers a wide range of concerns, including the problem of skepticism in the science of emotion, the problem of the underdetermination of a theory by the evidence, the question of the place of ordinary intuitions and ordinary language for a science of emotion, the mind-body problem, the hard problem of consciousness, the meta-hard problem of consciousness, the problem of intentionality, questions about the rationality of emotions and whether emotions can be a vehicle for knowledge, and the debate between cognitive and noncognitive theories in the philosophy of emotion. (shrink)

Girard and Reynolds independently invented System F to handle problems in logic and computer programming language design, respectively. Viewing F in the Curry style, which associates types with untyped lambda terms, raises the questions of typability and type checking. Typability asks for a term whether there exists some type it can be given. Type checking asks, for a particular term and type, whether the term can be given that type. The decidability of these problems has (...) been settled for restrictions and extensions of F and related systems and complexity lower-bounds have been determined for typability in F, but this report is the first to resolve whether these problems are decidable for System F. This report proves that type checking in F is undecidable, by a reduction from semi-unification, and that typability in F is undecidable, by a reduction from type checking. Because there is an easy reduction from typability to type checking, the two problems are equivalent. The reduction from type checking to typability uses a novel method of constructing lambda terms that simulate arbitrarily chosen type environments. All of the results also hold for the λI-calculus. (shrink)

A two-stage procedure is described which induces type-logical grammar lexicons from sentences annotated with skeletal terms of the simply typed lambda calculus. First, a generalized formulae-as-types correspondence is exploited to obtain all the type-logical proofs of the sample sentences from their lambda terms. The resulting lexicons are then optimally unified. The first stage constitutes the semantic bootstrapping (Pinker, Language Learnability and Language Development, Harvard University Press, 1984), while the unification procedure of Buszkowski and Penn represents a first (...) attempt at structure-dependent distributional learning of the syntactic and semantic categories. This effort extends earlier induction procedures (Buszkowski and Penn, 1990, Studia Logica 49, 431–454; Kanazawa, 1998, CSLI Publications and the European Association for Logic, Language and Information) for classical categorial grammar to at first the non-associative Lambek calculus, and then to a large class of type logics enriched by modal operators and structural rules. (shrink)

A two-stage procedure is described which induces type-logical grammar lexicons from sentences annotated with skeletal terms of the simply typed lambda calculus. First, a generalized formulae-as-types correspondence is exploited to obtain all the type-logical proofs of the sample sentences from their lambda terms. The resulting lexicons are then optimally unified. The first stage constitutes the semantic bootstrapping (Pinker, Language Learnability and Language Development, Harvard University Press, 1984), while the unification procedure of Buszkowski and Penn represents a first (...) attempt at structure-dependent distributional learning of the syntactic and semantic categories. This effort extends earlier induction procedures (Buszkowski and Penn, 1990, Studia Logica 49, 431–454; Kanazawa, 1998, CSLI Publications and the European Association for Logic, Language and Information) for classical categorial grammar to at first the non-associative Lambek calculus, and then to a large class of type logics enriched by modal operators and structural rules. (shrink)

This paper develops a framework for TAG (Tree Adjoining Grammar) semantics that brings together ideas from different recent approaches. Then, within this framework, an analysis of scope is proposed that accounts for the different scopal properties of quantifiers, adverbs, raising verbs and attitude verbs. Finally, including situation variables in the semantics, different situation binding possibilities are derived for different types of quantificational elements.

We show that some common varieties of modal K4-algebras have finitary unification type, thus providing effective best solutions for equations in free algebras. Applications to admissible inference rules are immediate.

Contact Logics provide a natural framework for representing and reasoning about regions in several areas of computer science. In this paper, we focus our attention on reasoning methods for Contact Logics and address the satisfiability problem and the unifiability problem. Firstly, we give sound and complete tableaux-based decision procedures in Contact Logics and we obtain new results about the decidability/complexity of the satisfiability problem in these logics. Secondly, we address the computability of the unifiability problem in Contact Logics and we (...) obtain new results about the unification type of the unifiability problem in these logics. (shrink)

Some theorists of normative explanation argue that we can make sense of debates between first-order moral theories such as consequentialism and its rivals only if we understand their explanations of why the right acts are right and the wrong acts are wrong as generative (e.g. grounding) explanations. Others argue that the standard form of normative explanation is, instead, some kind of unification. Neither sort of explanatory monism can account for all the explanations of particular moral facts that moral theorists (...) seek to state and defend. This paper argues that we can do better if we accept normative explanatory pluralism, the view that at least some particular explananda in normative inquiry have more than one type of correct complete explanation. Such pluralism is supported by what goes on in actual moral inquiry, parallels an independently plausible form of pluralism about scientific explanation, and can offer principled responses to central objections. (shrink)

Is the universe really governed by a small set of unifying fundamental laws, as many thinkers have claimed since ancient times? Philosophers who call themselves naturalists believe that the way to settle such questions is to look carefully at what empirical science tells us. In this book, Margaret Morrison argues that if we really do this, we find that science currently does not give us any reason to believe the common picture of the world in which everything can be reduced (...) to a vanishingly small set of entities and forces. Like Nancy Cartwright and John Dupree, Morrison believes that science reveals a world of numerous different sorts of entities and processes, described by different sorts of explanation. Trying to come up with unified descriptions of phenomena does play an important role in science, says Morrison, but there are different types of unification. The sort in which one set of entities can be reductively identified with another occurs rarely. What we find more often are various ways of subsuming different phenomena under similar mathematical formalisms. An urge to unify, in different guises, is an important research motivator, Morrison argues, but it is not the sort of monolithic engine of science that many make it out to be. (shrink)

Cancer is not one, but many diseases, and each is a product of a variety of causes acting (and interacting) at distinct temporal and spatial scales, or “levels” in the biological hierarchy. In part because of this diversity of cancer types and causes, there has been a diversity of models, hypotheses, and explanations of carcinogenesis. However, there is one model of carcinogenesis that seems to have survived the diversification of cancer types: the multi-stage model of carcinogenesis. This paper examines the (...) history of the multistage theory, and uses the theory as a case study in the limits and goals of unification as a theoretical virtue, comparing and contrasting it with “integrative” research. (shrink)

This paper gives a simple method for providing categorial brands of feature-based unification grammars with a model-theoretic semantics. The key idea is to apply the paradigm of fibred semantics (or layered logics, see Gabbay (1990)) in order to combine the two components of a feature-based grammar logic. We demonstrate the method for the augmentation of Lambek categorial grammar with Kasper/Rounds-style feature logic. These are combined by replacing (or annotating) atomic formulas of the first logic, i.e. the basic syntactic types, (...) by formulas of the second. Modelling such a combined logic is less trivial than one might expect. The direct application of the fibred semantics method where a combined atomic formula like np (num: sg & pers: 3rd) denotes those strings which have the indicated property and the categorial operators denote the usual left- and right-residuals of these string sets, does not match the intuitive, unification-based proof theory. Unification implements a global bookkeeping with respect to a proof whereas the direct fibring method restricts its view to the atoms of the grammar logic. The solution is to interpret the (embedded) feature terms as global feature constraints while maintaining the same kind of fibred structures. For this adjusted semantics, the anticipated proof system is sound and complete. (shrink)

Requirements for a Fundamental Physical Theory. The search for a so-called ‘Theory of Everything’ which should lead to the unification of all fundamental forces is seen, at present, as a matter of priority within theoretical high-energy physics. Some physicist identify this Theory of Everything today with aspecific type of superstring theory or its intended conceptual continuation, called M-Theory. The objective of this article is the discussion of the requirements a fundamental physical theory has to comply with. This question (...) can only be clarified if one takes into account that the claim that a physical theory is all-encompassing takes forgranted some tacit prerequisites which concern the conceptual and epistemological foundations of science and, not least, the question for the realizability of its reductionistic unity. (shrink)