Two of the most well-known belief contraction operators are partial meet contractions (PMCs) and kernel contractions (KCs). In this paper we propose two new classes of contraction operators, namely the class of generalized partial meet contractions (GPMC) and the class of generalized kernel contractions (GKC), which strictly contain the classes of PMCs and of KCs, respectively. We identify some extra conditions that can be added to the definitions of GPMCs and of GKCs, which give rise to (...) some interesting subclasses of those classes of functions, namely the classes of extensional and of uniform GPMCs/GKCs. In the context of contractions on belief sets the classes of partial meet contractions, uniform GPMCs and extensional GPMCs are all identical. Nevertheless, when considered as operations on belief bases, the class of uniform GPMCs coincides with the class of partial meet contractions, but the extensional GPMCs constitute a new kind of belief base contraction functions whose characterizing postulate of irrelevance of syntax is extensionality—the same postulate of irrelevance of syntax which occurs in the classical axiomatic characterization of partial meet contractions for belief sets—rather than the postulate of uniformity—which is the irrelevance of syntax postulate used in the axiomatic characterization for partial meet contractions on belief bases. Analogous results are obtained regarding the classes of extensional and of uniform GKCs. We present the interrelations in the sense of inclusion among all the new classes of operators presented in this paper and several well known classes of PMCs and of KCs. (shrink)

Kernel contraction is a natural nonrelational generalization of safe contraction. All partial meet contractions are kernel contractions, but the converse relationship does not hold. Kernel contraction is axiomatically characterized. It is shown to be better suited than partial meet contraction for formal treatments of iterated belief change.

This paper focuses on the extension of AGM that allows change for a belief base by a set of sentences instead of a single sentence. In [FH94], Fuhrmann and Hansson presented an axiomatic for Multiple Contraction and a construction based on the AGM Partial Meet Contraction. We propose for their model another way to construct functions: Multiple Kernel Contraction, that is a modification of Kernel Contraction, proposed by Hansson [Han94] to construct classical AGM contractions (...) and belief base contractions. This construction works out the unsolved problem pointed out by Hansson in [Han99, pp. 369]. (shrink)

This paper focuses on the extension of AGM that allows change for a belief base by a set of sentences instead of a single sentence. In [FH94], Fuhrmann and Hansson presented an axiomatic for Multiple Contraction and a construction based on the AGM Partial Meet Contraction. We propose for their model another way to construct functions: Multiple Kernel Contraction, that is a modification of Kernel Contraction, proposed by Hansson [Han94] to construct classical AGM contractions (...) and belief base contractions. This construction works out the unsolved problem pointed out by Hansson in [Han99, pp. 369]. (shrink)

Blockage contraction is an operation of belief contraction that acts directly on the outcome set, i.e. the set of logically closed subsets of the original belief set K that are potential contraction outcomes. Blocking is represented by a binary relation on the outcome set. If a potential outcome X blocks another potential outcome Y, and X does not imply the sentence p to be contracted, then Y ≠ K ÷ p. The contraction outcome K ÷ p (...) is equal to the (unique) inclusion-maximal unblocked element of the outcome set that does not imply p. Conditions on the blocking relation are specified that ensure the existence of such a unique inclusion-maximal set for all sentences p. Blockage contraction is axiomatically characterized and its relations to AGM-style operations are investigated. In a finite-based framework, every transitively relational partial meet contraction is also a blockage contraction. (shrink)

We can often specify how we would contract by a certain sentence by saying that this contraction would coincide with some other contraction that we know how to perform. We can for instance clarify that our contraction by p&q would coincide with our contraction by p, or by q, or by {p, q}. In a framework where the set of potential outcomes is known, some contractions are “self-evident” in the sense that there is only one serious (...) candidate that can be the outcome of such a contraction. Contraction by a specific contractee (sentence or set of sentences to be contracted) is bootstrapped if it is specified by saying that it coincides with some such self-evident contraction. For a wide range of (multiple) contraction operators, contractions by any contractee can be bootstrapped. This means that the selection mechanism (selection function, incision function, etc.) can be replaced by a function called a bootstrapping selector that assigns to each contractee some “self-evident” contractee that yields the same outcome. With bootstrapping we can eliminate traditional extralogical components in contraction (e.g., selection functions) and replace them by bootstrapping selectors that reflect more closely the ways in which we actually reason and argue about belief contraction. (shrink)

The basic assumption of repertoire contraction is that only some of the logically closed subsets of the original belief set are viable as contraction outcomes. Contraction takes the form of choosing directly among these viable outcomes, rather than among cognitively more far-fetched objects such as possible worlds or maximal consistent subsets of the original belief set. In this first investigation of repertoire contraction, postulates for various variants of the operation are introduced. Necessary and sufficient conditions are (...) given for when repertoire contraction coincides with AGM contraction or with operations generated by AGM-style contraction on a belief base. A close connection is shown to hold between repertoire contraction and specified meet contraction. (shrink)

Scientific inquiry is represented as a process of rational hypothesis revision in the face of data. For the concept of rationality, we rely on the theory of belief dynamics as developed in [5, 9]. Among other things, it is shown that if belief states are left unclosed under deductive logic then scientific theories can be expanded in a uniform, consistent fashion that allows inquiry to proceed by any method of hypothesis revision based on "kernel" contraction. In contrast, if (...) belief states are closed under logic, then no such expansion is possible. (shrink)

Scientific inquiry is represented as a process of rational hypothesis revision in the face of data. For the concept of rationality, we rely on the theory of belief dynamics as developed in [5, 9]. Among other things, it is shown that if belief states are left unclosed under deductive logic then scientific theories can be expanded in a uniform, consistent fashion that allows inquiry to proceed by any method of hypothesis revision based on “kernel” contraction. In contrast, if (...) belief states are closed under logic, then no such expansion is possible. (shrink)

This thesis consists in six articles and a comprehensive summary. • The pourpose of the summary is to introduce the AGM theory of belief change and to exemplify the diversity and significance of the research that has been inspired by the AGM article in the last 25 years. The research areas associated with AGM was divided in three parts: criticisms, where we discussed some of the more common criticisms of AGM. Extensions where the most common extensions and variations of AGM (...) are presented and applications where we provided an overview of applications and connections with other areas of research. • Article I elaborates on the connection between partial meet contractions [AGM85] and kernel contractions [Han94a] in belief change theory. Also both functions are equivalent in belief sets, there are notequivalent in belief bases. A way to define incision functions from selection functions and vice versa is presented. It is explained under which conditions there are exact correspondences between selection and incision functions so that the same contraction operations can be obtained by using either of them. • Article II proposes an axiomatic characterization for ensconcement-based contraction functions, belief base functions proposed byWilliams and relates this function with other kinds of base contraction functions. • Article III adapts the Fermé and Hansson model of Shielded Contraction [FH01] as well as Hansson et all Credibility-Limited Revision [HFCF01] for belief bases, to join two of the many variations of the AGM model [AGM85], i.e. those in which knowledge is represented through belief bases instead of logic theories, and those in which the object of the epistemic change does not get the priority over the existing information as it is the case in the AGM model. • Article IV introduces revision by comparison a refined method for changing beliefs by specifying constraints on the relative plausibility of propositions. Like the earlier belief revision models, the method proposed is a qualitative one, in the sense that no numbers are needed in order to specify the posterior plausibility of the new information. The method uses reference beliefs in order to determine the degree of entrenchment of the newly accepted piece of information. Two kinds of semantics for this idea are proposed and a logical characterization of the new model is given. • Article V focuses on the extension of AGM that allows change for a belief base by a set of sentences instead of a single sentence. In [FH94], Fuhrmann and Hansson presented an axiomatic for Multiple Contraction and a construction based on the AGM Partial Meet Contraction. This essay proposes for their model another way to construct functions: Multiple Kernel Contraction, that is a modification of Kernel Contraction,proposed by Hansson [Han94a] to construct classical AGM contractions and belief base contractions. • Article VI relates AGM model with the DFT model proposed by Carlos Alchourrón [Alc93]. Alchourrón devoted his last years to the analysis of the notion of defeasible conditionalization. His definition of the defeasible conditional is given in terms of strict implication operator and a modal operator f which is interpreted as a revision function at the language level. This essay points out that this underlying revision function is more general than AGM revision. In addition, a complete characterization of that more general kind of revision that permits to unify models of revision given by other authors is given. (shrink)

We introduce a new operator, called rational evaluation, in belief change. The operator evaluates new information according to the agent’s core beliefs, and then exports the plausible part of the new information. It belongs to the decision module in belief change. We characterize rational evaluation by axiomatic postulates and propose two functional constructions for it, based on the well-known constructions of kernel sets and remainder sets, respectively. The main results of the paper are two representation theorems with respect to (...) the two functional constructions. We also compare and connect the evaluation operator with some related operators in belief revision, including contraction, set contraction, and prioritized multiple revision. (shrink)

The paper connects two central ethical views, both with a rich tradition, sentimentalism and contractualism. From the former, it also borrows the response-dependentist metaphysics. The idea of combining the two has been sketched before, but not systematically and explicitly; for instance, in various comments on classical authors, especially on Kant and elsewhere, most prominently in Habermas. Here is the kernel of the present proposal. Our initial practical intuitions are emotion-based and the values, when detected, are response-dependent. This is the (...) starting point borrowed from sentimentalism. These intuitions get improved by reflection, and by dialogue that crucially involves perspective taking. If all goes well, this results in insights, in particular into principles that all rational parties can agree about in a kind of “contract.” This brings two traditions, the one of David Hume and Adam Smith, and the other of Kant, together. The resulting theory would be a kind of sentimentalist, response-dependentist contractualism. (shrink)

The Motoneurone and its Muscle Fibres presents a state-of-the-art summary of knowledge concerning the motoneurones, vital for innervating and commanding skeletal muscles. No muscle action would be possible without motoneurones. These cells are therefore absolutely essential for the execution of normal behaviour and for life support. It is their degeneration that leads to various kinds of motoneurone disease that are often ultimately lethal. However, the study of motoneurones is also important for general insights as to how neurones work, because the (...) motoneurone is probably the best understood kind of nerve cell so far in neuroscience. Motoneurones of the spinal cord were the first type of central nerve cell to be subjected to detailed physiological measurements, and much is known about how their activity is regulated by synapses from other central neurones. For most of the individual neurones within the central nervous system, the precise functional tasks are difficult to define. However, for motoneurones much is now known about their short- and long-term interactions with their main targets, the skeletal muscle fibres. Functions of neurones must be analyzed in relation to the response properties of their target cells. Therefore, this book deals with both, summarizing classical as well as recent knowledge concerning the motoneurone and its muscle fibres. This is the first time that so many aspects of this broad subject matter are treated in one comprehensive monograph. (shrink)

Introduction -- "Every Legitimate Government is Republican": Rousseau's Debt to and Departure from Montesquieu on Republicanism -- What if There is no Legislator? Rousseau's History of the Government of Geneva -- Rousseau's Republican Citizenship: The Moral Psychology of The Social Contract -- Rousseau's negative liberty: Themes of domination and skepticism in The Social Contract -- Rousseau's Ancient Ends of Legislation: Liberty, Equality (& Fraternity) -- Property and Possession in Rousseau's Social Contract -- Political Equality Among Unequals -- On the Primacy (...) of Peoplehood: Nations and Nationalism in Rousseau's Social Contract -- Rousseau on Voting and Electoral Laws -- Rousseau and the puzzle of the Roman Republic -- Rousseau's Case against Democracy -- Rousseau's Dilemma or "Of Civil Religion" -- Entreating the Political: Politics and Theology in Rousseau's Social Contract -- Civil Religion and Political Unity: Social Contract 4.8. (shrink)

Ranking theory delivers an account of iterated contraction; each ranking function induces a specific iterated contraction behavior. The paper shows how to reconstruct a ranking function from its iterated contraction behavior uniquely up to multiplicative constant and thus how to measure ranks on a ratio scale. Thereby, it also shows how to completely axiomatize that behavior. The complete set of laws of iterated contraction it specifies amend the laws hitherto discussed in the literature.

This essay demonstrates proof-theoretically the consistency of a type-free theoryC with an unrestricted principle of comprehension and based on a predicate logic in which contraction (A (A B)) (A B), although it cannot holds in general, is provable for a wide range ofA's.C is presented as an axiomatic theoryCH (with a natural-deduction equivalentCS) as a finitary system, without formulas of infinite length. ThenCH is proved simply consistent by passing to a Gentzen-style natural-deduction systemCG that allows countably infinite conjunctions and (...) in which all theorems ofCH are provable.CG is seen to be a consistent by a normalization argument. It also shown that in a senseC is highly non-extensional. (shrink)

In 1909, Ehrenfest published a note in the Physikalische Zeitschrift showing that a Born rigid cylinder could not be set into rotation without stresses, as elements of the circumference would be contracted but not the radius. Ignatowski and Varićak challenged Ehrenfest’s result in the same journal, arguing that the stresses would emerge if length contraction were a real dynamical effect, as in Lorentz’s theory. However, no stresses are expected to arise, according to Einstein’s theory, where length contraction is (...) only an apparent effect due to an arbitrary choice of clock synchronization. Ehrenfest and Einstein considered this line of reasoning dangerously misleading and took a public stance in the Physikalische Zeitschrift, countering that relativistic length contraction is both apparent and real. It is apparent since it disappears for the comoving observer, but it is also real since it can be experimentally verified. By drawing on his lesser-known private correspondence with Varićak, this paper shows how Einstein used the Ehrenfest paradox as a tool for an ‘Einsteinian pedagogy’. Einstein’s argumentative stance is contrasted with Bell’s use of the Dewan-Beran thread-between-spaceships paradox to advocate for a ‘Lorentzian pedagogy’. The paper concludes that the disagreement between the two ways of ‘teaching special relativity’ stems from divergent interpretations of philosophical categories such as ‘reality’ and ‘appearance’. (shrink)

This paper is concerned with formal aspects of the logic of theory change, and in particular with the process of shrinking or contracting a theory to eliminate a proposition. It continues work in the area by the authors and Peter Gärdenfors. The paper defines a notion of safe contraction of a set of propositions, shows that it satisfies the Gärdenfors postulates for contraction and thus can be represented as a partial meet contraction, and studies its properties both (...) in general and under various natural constraints. (shrink)

In this paper we investigate AGM belief contraction operators by using the tools of algebraic logic. We generalize the notion of contraction to arbitrary finitary propositional logics, and we show how to switch from a syntactic-based approach to a semantic one. This allows to build a solid bridge between the validity of AGM postulates in a propositional logic and specific algebraic properties of its intended algebraic counterpart. Such a connection deserves particular attention when we deal with maxichoice contractions, (...) as studied in the final part of the paper. (shrink)

In the most common approaches to belief dynamics, states of belief are represented by sets that are closed under logical consequence. In an alternative approach, they are represented by non-closed belief bases. This representation has attractive properties not shared by closed representations. Most importantly, it can account for repeated belief changes that have not yet been satisfactorily accounted for in the closed approach.

Full meet contraction, that was devised by Carlos Alchourrón and David Makinson in the early 1980' s, has often been overlooked since it is not in itself a plausible contraction operator. However, it is a highly useful building-block in the construction of composite contraction operators. In particular, all plausible contraction operators can be reconstructed so that the outcome of contracting a belief set K by a sentence p is defined as K ∼ f, where ∼ is (...) full meet contraction and f a sentential selector, i.e. a function to and from sentences. This paper investigates the logic of full meet contraction. Seven properties of this operation are presented that contribute to making it useful as a building-block: Full meet contraction is a purely logical operation. It retains finitebasedness of the belief set. It is the inclusion-maximal contraction that removes all sentences that can contribute to implying the input sentence. It is the inclusion-maximal contraction that removes all non-tautologous consequences of the input sentence. Almost all contractions can be reconstructed as full meet contraction. Full meet contraction allows for recovery of the input sentence. Full meet contraction provides a unified account of multiple and singleton contraction. La llamada full meet contraction, creada por Carlos Alchourrón y David Makinson en los comienzos de los ' 80, ha sido a menudo desestimada puesto que ella no constituye un operador de contracción plausible. De todas formas ella es altamente útil en la construcción de operadores de contracción compuestos. En particular, todos los operadores de contracción plausibles pueden ser reconstruidos de forma tal que la contracción de un conjunto de creencias K por una sentencia p sea definida como K ∼ f, donde ∼ es una full meet contraction y f un selector de sentencias, i.e., una función de sentencias a sentencias. En este trabajo investigamos la lógica de la full meet contraction. Se presentan siete propiedades de esta operación que contribuyen a hacerla útil como building-block: Full meet contraction es una operación puramente lógica. Ella retiene la finit- basednes del conjunto de creencias. Ella es la máxima-inclusiva de las contracciones que elimina todas las sentencias que pueden contribuir a implicar la input-sentence. Es la contracción maximal inclusiva que elimina todas las consecuencias no tautológicas de la input-sentence. Casi todas las contracciones pueden ser reconstruidas como full-meet contractions. Full meet contraction permite la recuperación de la input-sentence. Full meet contracción da cuenta en forma unificada de las contracciones múltiples y singulares. (shrink)

A logic is said to be contraction free if the rule from A→(A→B) to A→B is not truth preserving. It is well known that a logic has to be contraction free for it to support a non-trivial naïve theory of sets or of truth. What is not so well known is that if there is another contracting implication expressible in the language, the logic still cannot support such a naïve theory. A logic is said to be robustly (...) class='Hi'>contraction free if there is no such operator expressible in its language. We show that a large class of finitely valued logics are each not robustly contraction free, and demonstrate that some other contraction free logics fail to be robustly contraction free. Finally, the sublogics of Łω (with the standard connectives) are shown to be robustly contraction free. (shrink)

The outcome set of a belief change operator is the set of outcomes that can be obtained with it. Axiomatic characterizations are reported for the outcome sets of the standard AGM contraction operators and eight types of base-generated contraction. These results throw new light on the properties of some of these operators.

As a fundamental feature of our existence, melancholy is an inescapable characteristic of our ontological constitution. However, there is a distance between the clinical condition of melancholia and the human feeling, the capacity to feel sorrow and nostalgia. In this sense, melancholy and melancholia are similar but different. During the XIX century just few among philosophers have tried to described melancholy in terms of disorder, using philosophical tools rather than clinical definitions, drifting the accent from melancholy to melancholia. Hegel has (...) been one of them, one that has seen inside the depth of human being in order to understand and describe what is the “the nocturnal point of the contraction”: melancholia, in terms of clinical condition. The philosophical exploration of madness and its parameters is essentially an ontological project: this is how Hegel addresses “the Concept of derangement in general” and melancholia in particular, anticipating most of Freud’s consideration on this topic. (shrink)

There is an apparent contradiction within Levinas’s work: on the one hand, Levinas upholds an account of existence that seemingly requires a creation narrative, while maintaining, on the other hand, that an account of the ethical import of that existence needs no recourse to the divine. This seeming contradiction results from a fundamental misunderstanding concerning Levinas’s account of creation and its logical consequences concerning the divine. This paper aims to clarify this misunderstanding by exploring the similarities between and influence of (...) F. W. J. Schelling’s work on Levinas’s thereby providing a more complete picture of both author’s respective accounts of genesis and the existence of God. (shrink)

In some recent papers, the authors and Peter Gärdenfors have defined and studied two different kinds of formal operation, conceived as possible representations of the intuitive process of contracting a theory to eliminate a proposition. These are partial meet contraction (including as limiting cases full meet contraction and maxichoice contraction) and safe contraction. It is known, via the representation theorem for the former, that every safe contraction operation over a theory is a partial meet (...) class='Hi'>contraction over that theory. The purpose of the present paper is to study the relationship more finely, by seeking an explicit map between the component orderings involved in each of the two kinds of contraction. It is shown that at least in the finite case a suitable map exists, with the consequence that the relational, transitively relational, and antisymmetrically relational partial meet contraction functions form identifiable subclasses of the safe contraction functions, over any theory finite modulo logical equivalence. In the process of constructing the map, as the composition of four simple transformations, mediating notions of bottom and top contraction are introduced. The study of the infinite case remains open. (shrink)

Agents need to be able to change their beliefs; in particular, they should be able to contract or remove a certain belief in order to restore consistency to their set of beliefs, and revise their beliefs by incorporating a new belief which may be inconsistent with their previous beliefs. An influential theory of belief change proposed by Alchourron, G¨ardenfors and Makinson (AGM) [1] describes postulates which a rational belief revision and contraction operations should satisfy. The AGM postulates have been (...) perceived as characterising idealised rational reasoners, and the corresponding belief change operations are considered unsuitable for implementable agents due to their high computational cost [3]. The main result of this paper is showing that an efficient (linear time) belief contraction operation nevertheless satisfies all but one of the AGM postulates for contraction. This contraction operation is defined for a realistic rule-based agent which can be seen as a reasoner in a very weak logic; although the agent’s beliefs are deductively closed with respect to this logic, checking consistency and tracing dependencies between beliefs is not computationally expensive. Finally, we give a non-standard definition of belief revision in terms of contraction for our agent. (shrink)

The Fitzgerald-Lorentz contraction hypothesis, proposed as an explanation of the Michelson-Morley result, fails to account for the Kennedy-Thorndike result. Hence, Grünbaum argues, the hypothesis has been falsified. However, the contraction hypothesis as formulated by Lorentz is false for the very fundamental reason that it entails a contradiction, namely, the consequence that light waves must have a variable velocity along what by definition is taken to be a rest length. Furthermore, the attempt to resolve this contradiction by coupling the (...) Fitzgerald-Lorentz contraction with the hypothesis that clock rates are a function of velocity, is open to a sound, methodological objection. The Michelson-Morley result is fully satisfied, provided only that the lengths of the interferometer arms, in the longitudinal and transverse positions, are thought to be related to one another in a certain ratio, and this ratio may be interpreted as a contraction in both arms. Since this twofold contraction hypothesis suffices to explain both the Michelson-Morley and the Kennedy-Thorndike results, and since it entails no contradiction, there is no need to correct both the length of rods and the rate of clocks. Therefore, the combined clock-rod hypothesis, and with it the Fitzgerald-Lorentz contraction hypothesis, must be rejected. (shrink)

Sven-Ove Hansson and Erik Olsson studied in Hansson and Olsson, 103–119 1995) the logical properties of an operation of contraction first proposed by Isaac Levi in Levi. They provided a completeness result for the simplest version of contraction that they call Levi-contraction but left open the problem of characterizing axiomatically the more complex operation of value-based contraction or saturatable contraction. In this paper we propose an axiomatization for this operation and prove a completeness result for (...) it. We argue that the resulting operation is better behaved than various rival operations of contraction defined in recent years. (shrink)

Smooth muscle cells squeeze the blood back to your heart, raise the hackles on your neck and change the F‐stop of your eyes. The past year has provided penetrating new insights into their mechanism of contraction.

Background: The proprioceptive neuromuscular facilitation reciprocal contraction pattern has the potential to increase the maximum rate of torque development. However, it is a more complex resistive exercise task and may interfere with improvements in the maximum rate of torque development due to motor skill learning, as observed for unidirectional contractions. The purpose of this study was to examine the cost-benefit of using the PNF exercise technique to increase the maximum rate of torque development.Methods: Twenty-six participants completed isometric maximal extension-to-flexion (...) or flexion-only contractions at the wrist. Ten of the assigned contractions were performed on each of three sessions separated by 48-h for skill acquisition. Retention was assessed with 5 contractions performed 2-weeks after acquisition. Torque and surface electromyographic activity were analyzed for evidence of facilitated contractions between groups, as well as alterations in muscle coordination assessed across test sessions. The criterion measures were: mean maximal isometric wrist flexion toque; the maximal rate of torque development ; root-mean-square error variability of the rate of torque versus torque phase-plane; the rate of wrist flexion muscle activation ; a coactivation ratio for wrist flexor and extensor sEMG activity; and wrist flexor electromechanical delay.Results: There were no significant differences between groups with respect to maximal wrist flexion torque, dτ/dtmax or RMSE variability of torque trajectories. Both groups exhibited a progressive increase in maximal strength and in dτ/dtmax from the start of acquisition to retention. RMSE was lowest after a 2-week rest interval. There were no significant differences between groups in the rate of muscle activation or the coactivation ratio. There was a reduction in coactivation that was retained after a 2-week rest interval. Alternatively, EMD was significantly greater in the experimental group across all sessions. However, both groups had a similar pattern of improvement to the third consecutive day of testing, but returned close to baseline value after the 2-week rest interval.Discussion: The wrist extension-to-flexion contraction pattern did not result in a greater maximal rate of torque development than simple contractions of the wrist flexors. There was no difference between groups with respect to motor skill learning. The main adaptation in neuromotor control was a decrease in coactivation, not the maximal rate of muscle activation. (shrink)

This paper offers a particular intuitionistic negation completion of Urquhart's system C resulting in a super-intuitionistic contractionless propositional logic equivalent to Dummett's LC without contraction.

Summary A recurrent theme in the philosophical literature on the special theory of relativity is the question as to the reality of the Lorentz contraction. It is often suggested that there is a difference between the Lorentz-FitzGerald contraction in the pre-relativistic ether theory and the Lorentz contraction from special relativity in the sense that the former is a real contraction of matter conditioned by dynamical laws, whereas the latter should be compared with the apparent changes in (...) the size of objects when the perspective of the observer changes. It is here shown, however, that the same laws of nature which are operative in the Lorentz-FitzGerald contraction also condition the relativistic Lorentz contraction. The relevant distinction therefore is not between the reality of the two contractions. What is at issue is the difference in explanatory structure of the pre-relativistic theory on the one hand and the special theory of relativity on the other. In the course of the argument the question of the conventionality of simultaneity is also discussed. (shrink)

In this paper, a semantics for predicate logics without the contraction rule will be investigated and the completeness theorem will be proved. Moreover, it will be found out that our semantics has a close connection with Beth-type semantics.

The aim of this paper is to show that the implicational fragment BKof the intuitionistic propositional calculus (IPC) without the rules of exchange and contraction has the finite model property with respect to the quasivariety of left residuation algebras (its equivalent algebraic semantics). It follows that the variety generated by all left residuation algebras is generated by the finite left residuation algebras. We also establish that BKhas the finite model property with respect to a class of structures that constitute (...) a Kripke-style relational semantics for it. The results settle a question of Ono and Komori [OK85]. (shrink)

Schopenhauer's claim that the essence of the world consists inWilleencounters well-known difficulties. Of particular importance is the conflict of this metaphysical claim with his restrictive account of conceptuality. This paper attempts to make sense of Schopenhauer's position by restoring him to the context of post-Kantian debate, with special attention to the early notebooks andFourfold Root of the Principle of Sufficient Reason. On the reconstruction suggested here, Schopenhauer's philosophical project should be understood in light of his rejection of post-Kantian metaphilosophy and (...) his opposition to German Idealism. (shrink)

This article presents Catherine Malabou and Alain Badiou as theorists of contraction and its related operations of self-reflexivity and infinite iteration. Trading on these commonalities, the article hopes to draw out Malabou’s and Badiou’s respective formalist commitments. On Badiou’s side, it sharpens the question of what is at stake in something as regulated as a “procedure”; on Malabou’s, it recognizes formal stakes to plasticity that often go unrecognized because of her penchant for biology. The article then concludes with a (...) broad comparison of these two thinkers in terms of their accounts of potential and imagines the critiques each might leverage against the other. Where Malabou might well regard Badiou to be too tightly constraining the shape of the future, Badiou is likely to find in Malabou one more instance of a naïve democratic materialism. (shrink)

Evidence is reviewed here that inositol (1, 4, 5) trisphosphate (Ins P3) is a key signal in translating the electrophysiological event in muscle stimulation into the molecular‐mechanical events of contraction. Not least, these findings raise questions about the suitability of the term ‘second messenger’.

Traction forces developed by most cell types play a significant role in the spatial organisation of biological tissues. However, due to the complexity of cell-extracellular matrix interactions, these forces are quantitatively difficult to estimate without explicitly considering cell properties and extracellular mechanical matrix responses. Recent experimental devices elaborated for measuring cell traction on extracellular matrix use cell deposits on a piece of gel placed between one fixed and one moving holder. We formulate here a mathematical model describing the dynamic behaviour (...) of the cell-gel medium in such devices. This model is based on a mechanical force balance quantification of the gel visco-elastic response to the traction forces exerted by the diffusing cells. Thus, we theoretically analyzed and simulated the displacement of the free moving boundary of the system under various conditions for cells and gel concentrations. This modelis then used as the theoretical basis of an experimental device where endothelial cells are seeded on a rectangular biogel of fibrin cast between two floating holders, one fixed and the other linked to a force sensor. From a comparison of displacement of the gel moving boundary simulated by the model and the experimental data recorded from the moving holder displacement, the magnitude of the traction forces exerted by the endothelial cell on the fibrin gel was estimated for different experimental situations. Different analytical expressions for the cell traction term are proposed and the corresponding force quantifications are compared to the traction force measurements reported for various kind of cells with the use of similar or different experimental devices. (shrink)

Mordechai Rotenberg, who is well known for his work on the pessimistic impact of Protestant ethics on the Western social sciences, presents here a systematic study derived from, and based on, Judeo-Hasidic ethics. Proceeding from the cabalistic-Hasidic concept of contraction (tzimtsum), according to which God's voluntary withdrawal into Himself to evacuate space for the world serves as a model for human behavior, Professor Rotenberg shows that it is not personal-social construction, but self- and social contraction, that explains how (...) the "is" and the "ought" of society are developed and maintained. (shrink)

We develop a vector space semantics for verb phrase ellipsis with anaphora using type-driven compositional distributional semantics based on the Lambek calculus with limited contraction of Jäger. Distributional semantics has a lot to say about the statistical collocation based meanings of content words, but provides little guidance on how to treat function words. Formal semantics on the other hand, has powerful mechanisms for dealing with relative pronouns, coordinators, and the like. Type-driven compositional distributional semantics brings these two models together. (...) We review previous compositional distributional models of relative pronouns, coordination and a restricted account of ellipsis in the DisCoCat framework of Coecke et al. :1079–1100, 2013). We show how DisCoCat cannot deal with general forms of ellipsis, which rely on copying of information, and develop a novel way of connecting typelogical grammar to distributional semantics by assigning vector interpretable lambda terms to derivations of LCC in the style of Muskens and Sadrzadeh Logical aspects of computational linguistics, Springer, Berlin, 2016). What follows is an account of ellipsis in which word meanings can be copied: the meaning of a sentence is now a program with non-linear access to individual word embeddings. We present the theoretical setting, work out examples, and demonstrate our results with a state of the art distributional model on an extended verb disambiguation dataset. (shrink)

ABSTRACT We consider evolution of knowledge bases caused by a sequence of basic steps of acquisition of a new information, either consistent or inconsistent with the original system. To make this process comply with the Principe of Minimal Change, a special evidence metric is introduced for measuring distance between states of knowledge. Then a novel semantics of knowledge bases is developed suggested by the heuristics of weighted maximally consistent subsets. The latter is efficiently applied to the processes of consistent and (...) inconsistent acquisition of knowledge, belief revision and contraction. (shrink)