What has science actually achieved? A theory of achievement should define what has been achieved, describe the means or methods used in science, and explain how such methods lead to such achievements. Predictive accuracy is one truth‐related achievement of science, and there is an explanation of why common scientific practices tend to increase predictive accuracy. Akaike’s explanation for the success of AIC is limited to interpolative predictive accuracy. But therein lies the strength of the general framework, for (...) it also provides a clear formulation of many open problems of research. (shrink)

The research aims to harness spatial interpolation techniques to produce maps with a high level of perceptual accuracy in representing the population data of the study area. This is achieved after exploring the statistical and spatial nature of the databases used, analyzing them, and determining their distribution using a variety of spatial data exploration tools available within the GIS (Geographic Information Systems) environment. These tools contribute to evaluating the characteristics, distribution, and analysis of data, including testing data distribution, (...) identifying its direction, and uncovering its spatial correlations. This highlights the importance of the study and understanding the distribution pattern of the population data in the study area, thereby facilitating the preparation of future that serve spatial organization by building spatial models for the numerical distribution of the data for age groups: young, middle-aged, and elderly, at the level of administrative units of the study area by relying on the inductive approach and the quantitative analysis approach. This is done using Geostatistical Analysis methods within the concept of spatial interpolation in GIS. The research also seeks to predict the population maps for Thi Qar Governorate by comparing spatial interpolation methods, namely Inverse Distance Weighting (IDW) and Simple Kriging (SK). The study concluded, after verifying the accuracy of the results using the Cross-Validation curve, that the Simple Kriging (SK) method is the most accurate model in spatial prediction of population data for representing the data of the young age group in the study area, as it had the lowest Root Mean Square Error (RMSE) of 10.012. It was followed by the Inverse Distance Weighting (IDW) method for representing the data of the elderly age group with an RMSE of 350.48. This indicates that the use of statistical criteria improves the accuracy of spatial interpolation and that the spatial prediction of the population data for the study area using the Simple Kriging (SK) method was more accurate than the Inverse Distance Weighting (IDW) method based on statistical indicators. (shrink)

To solve the problem that traditional trajectory prediction methods cannot meet the requirements of high-precision, multi-dimensional and real-time prediction, a 4D trajectory prediction model based on the backpropagation (BP) neural network was studied. First, the hierarchical clustering algorithm and the k-means clustering algorithm were adopted to analyze the total flight time. Then, cubic spline interpolation was used to interpolate the flight position to extract the main trajectory feature. The 4D trajectory prediction model was based on the BP neural network. (...) It was trained by Automatic Dependent Surveillance – Broadcast trajectory from Qingdao to Beijing and used to predict the flight trajectory at future moments. In this paper, the model is evaluated by the common measurement index such as maximum absolute error, mean absolute error and root mean square error. It also gives an analysis and comparison of the predicted over-point time, the predicted over-point altitude, the actual over-point time and the actual over-point altitude. The results indicate that the predicted 4D trajectory is close to the real flight data, and the time error at the crossing point is no more than 1 min and the altitude error at the crossing point is no more than 50 m, which is of high accuracy. (shrink)

Biometric identity systems are now a prominent feature of contemporary law enforcement, including in Europe. Often advanced on the premise of efficiency and accuracy, they have also been the subject of significant controversy. Much attention has focussed on longer-standing biometric data collection, such as finger-printing and facial recognition, foregrounding concerns with the impact such technologies can have on the nature of policing and fundamental human rights. Less researched is the growing use of voice recognition in law enforcement. This paper (...) examines the case of the recent Speaker Identification Integrated Project, a European wide initiative to create the first international and interoperable database of voice biometrics, now the third largest biometric database at Interpol. Drawing on Freedom of Information requests, interviews and public documentation, we outline the emergence and features of SiiP and explore how voice is recognised and attributed meaning. We understand Speaker Identification Integrated Project as constituting a particular ‘regime of recognition’ premised on the use of soft biometrics to disembed voice in order to optimise for difference. This, in turn, has implications for the nature and scope of law enforcement, people's position in society, and justice concerns more broadly. (shrink)

This article suggests an enhancement of the Masek circle model approach usually used to find a trade-off between modeling complexity, algorithm accuracy, and computational time, mainly for embedded systems where the real-time aspect is a high challenge. Moreover, most commercialized systems today frame iris regions by circles. This work led to several novelties: first, in the segmentation process, the corneal reflection removal method based on morphological reconstruction and pixel connectivity was implemented. Second, the picture size reduction was applied according (...) to nearest-neighbor interpolation. Third, the image gradient of the convolved-reduced picture was then generated using four proposed matrices. Fourth, and to reduce the complexity of the traditional method for the detection of the top and lower eyelids, a new method based on the Radon transform and the least squares fitting method was applied. Fifth, eyelashes were detected via the diagonal gradient and thresholding method. Monogenic signal was used in the feature extraction process. Finally, two distance measures were selected as a metric for recognition. Our experimental results using CASIA iris database V3.0 reveal that the proposed method provides a high performance in terms of speed and accuracy. Using dissimilarity modified Hamming distance, the accuracy of iris recognition was improved, with a false acceptance rate equal to 3% and a speed at least eight times as compared with the state of the art. (shrink)

This article puts forward a novel class of Bézier smooth semi-supervised support vector machines(BS4VMs) for classification. As is well known, semi-supervised support vector machine is introduced for dealing with quantities of unlabeled data in the real world. Labeled data is utilized to train the algorithm and then adapting it to classify the unlabeled data. However, the objective semi-supervised function is not differentiable globally. It is required to endure heavy burden in solving two quadratic programming problems with inversion matrix operation. To (...) solve this problem, the interpolation Bézier functions for replacing the non-smooth term have been investigated. Firstly, the development of the novel BS4VMs classifier is introduced. Then, the non-linear model and convergence analysis are presented. To show how the BS4VMs can be practically implemented, experiments on synthetic and real data sets are offered. The theoretical analysis and experiments comparisons clearly illustrate the BS4VMs are superior to the proposed methods in both cross-validation classification accuracy and calculating time. (shrink)

In order to solve the problem of low accuracy of pedestrian detection of real traffic cameras and high missed detection rate of small target pedestrians, this paper combines autoencoding neural network and AdaBoost to construct a fast pedestrian detection algorithm. Aiming at the problem that a single high-level output feature map has insufficient ability to express pedestrian features and existing methods cannot effectively select appropriate multilevel features, this paper improves the traditional AdaBoost algorithm structure, that is, the sample weight (...) update formula and the strong classifier output formula are reset, and the two-input AdaBoost-DBN classification algorithm is proposed. Moreover, in view of the problem that the fusion video is not smoothly played, this paper considers the motion information of the video object, performs pixel interpolation by motion compensation, and restores the frame rate of the original video by reconstructing the dropped interframe image. Through experimental research, we can see that the algorithm constructed in this paper has a certain effect. (shrink)

Knowledge demands more than accuracy: epistemologists are broadly agreed that those who know are non-accidentally right, satisfying some kind of safety condition. However, it is hard to formulate any adequate account of safety, and harder still to explain exactly why we care about it. This paper approaches the problem by looking at a concrete human cognitive capacity, face recognition, to see where epistemic safety shows up in it. Drawing on new models in artificial intelligence, and making a case that (...) human face recognition is relevantly similar, I argue that safety is a natural feature of successful generalization. The concluding section of the paper applies this lesson to the problem of our intuitive recognition of knowledge. (shrink)

This paper studies the properties and performance of models for estimating local probability distributions which are used as components of larger probabilistic systems — history-based generative parsing models. We report experimental results showing that memory-based learning outperforms many commonly used methods for this task (Witten-Bell, Jelinek-Mercer with fixed weights, decision trees, and log-linear models). However, we can connect these results with the commonly used general class of deleted interpolation models by showing that certain types of memory-based learning, including the (...) kind that performed so well in our experiments, are instances of this class. In addition, we illustrate the divergences between joint and conditional data likelihood and accuracy performance achieved by such models, suggesting that smoothing based on optimizing accuracy directError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMaply might greatly improve performance. (shrink)

In this paper, a repetitive control scheme of a 2-DOF robotic manipulator based on the improved cubic B-spline curve is proposed. Firstly, a repetitive controller for robotic manipulator is designed, which is composed of an iterative controller and disturbance observer. Then, an improved B-spline optimization scheme is introduced to divide the task of the robotic manipulator into three intervals. A correction function is added to each interval of cubic spline interpolation. Finally, a variety of cases are designed and simulated (...) by MATLAB. The experimental results show that, compared with the conventional B-spline, the improved B-spline has better performance in tracking accuracy and smoothness of motion trajectory. By changing the mechanism of the manipulator, the cases of different weights and lengths are designed. The experimental results in these cases show that the proposed scheme can be applied to most of the 2-DOF robotic manipulator control systems. (shrink)

Richard Pettigrew offers an extended investigation into a particular way of justifying the rational principles that govern our credences. The main principles that he justifies are the central tenets of Bayesian epistemology, though many other related principles are discussed along the way. Pettigrew looks to decision theory in order to ground his argument. He treats an agent's credences as if they were a choice she makes between different options, gives an account of the purely epistemic utility enjoyed by different sets (...) of credences, and then appeals to the principles of decision theory to show that, when epistemic utility is measured in this way, the credences that violate the principles listed above are ruled out as irrational. The account of epistemic utility set out here is the veritist's: the sole fundamental source of epistemic utility for credences is their accuracy. Thus, Pettigrew conducts an investigation in the version of epistemic utility theory known as accuracy-first epistemology. (shrink)

In Accuracy and the Laws of Credence Richard Pettigrew assumes a particular view of belief, which states that people don't have any other doxastic states besides credences. This is in tension with the popular position that people have both credences and outright beliefs. Pettigrew claims that such a dual view of belief is incompatible with the accuracy-first approach. I argue in this paper that it is not. This is good news for Pettigrew, since it broadens the appeal of (...) his framework. (shrink)

We discuss the interpolation property on some important families of non classical logics, such as intuitionistic, modal, fuzzy, and linear logics. A special paragraph is devoted to a generalization of the interpolation property, uniform interpolation.

We argue that subjective Bayesians face a dilemma: they must offend against the spirit of their permissivism about rational credence or reject the principle that one should avoid accuracy dominance.

A proof of the (propositional) Craig interpolation theorem for cut-free sequent calculus yields that a sequent with a cut-free proof (or with a proof with cut-formulas of restricted form; in particular, with only analytic cuts) with k inferences has an interpolant whose circuit-size is at most k. We give a new proof of the interpolation theorem based on a communication complexity approach which allows a similar estimate for a larger class of proofs. We derive from it several corollaries: (...) (1) Feasible interpolation theorems for the following proof systems: (a) resolution (b) a subsystem of LK corresponding to the bounded arithmetic theory S 2 2 (α) (c) linear equational calculus (d) cutting planes. (2) New proofs of the exponential lower bounds (for new formulas) (a) for resolution ([15]) (b) for the cutting planes proof system with coefficients written in unary ([4]). (3) An alternative proof of the independence result of [43] concerning the provability of circuit-size lower bounds in the bounded arithmetic theory S 2 2 (α). In the other direction we show that a depth 2 subsystem of LK does not admit feasible monotone interpolation theorem (the so called Lyndon theorem), and that a feasible monotone interpolation theorem for the depth 1 subsystem of LK would yield new exponential lower bounds for resolution proofs of the weak pigeonhole principle. (shrink)

A family of prepositional logics is considered to be intermediate between the intuitionistic and classical ones. The generalized interpolation property is defined and proved is the following.Theorem on interpolation. For every intermediate logic L the following statements are equivalent:(i) Craig's interpolation theorem holds in L, (ii) L possesses the generalized interpolation property, (iii) Robinson's consistency statement is true in L.

An interpolation theorem holds for many standard modal logics, but first order $S5$ is a prominent example of a logic for which it fails. In this paper it is shown that a first order $S5$ interpolation theorem can be proved provided the logic is extended to contain propositional quantifiers. A proper statement of the result involves some subtleties, but this is the essence of it.

We consider the propositional logic equipped withChellas stitoperators for a finite set of individual agents plus the historical necessity modality. We settle the question of whether such a logic enjoys restricted interpolation property, which requires the existence of an interpolant only in cases where the consequence contains no Chellas stit operators occurring in the premise. We show that if action operators count as logical symbols, then such a logic has restricted interpolation property iff the number of agents does (...) not exceed three. On the other hand, if action operators are considered to be nonlogical symbols, then the restricted interpolation fails for any number of agents exceeding one. It follows that unrestricted Craig interpolation also fails for almost all versions of stit logic. (shrink)

We introduce a notion of a real game (a generalisation of the Karchmer-Wigderson game (cf. [3]) and of real communication complexity, and relate this complexity to the size of monotone real formulas and circuits. We give an exponential lower bound for tree-like monotone protocols (defined in [4, Definition 2.2]) of small real communication complexity solving the monotone communication complexity problem associated with the bipartite perfect matching problem. This work is motivated by a research in interpolation theorems for prepositional logic (...) (by a problem posed in [5, Section 8], in particular). Our main objective is to extend the communication complexity approach of [4, 5] to a wider class of proof systems. In this direction we obtain an effective interpolation in a form of a protocol of small real communication complexity. Together with the above mentioned lower bound for tree-like protocols this yields as a corollary a lower bound on the number of steps for particular semantic derivations of Hall's theorem (these include tree-like cutting planes proofs for which an exponential lower bound was demonstrated in [2]). (shrink)

In this article we show that bi-intuitionistic predicate logic lacks the Craig Interpolation Property. We proceed by adapting the counterexample given by Mints, Olkhovikov and Urquhart for intuitionistic predicate logic with constant domains [13]. More precisely, we show that there is a valid implication $\phi \rightarrow \psi $ with no interpolant. Importantly, this result does not contradict the unfortunately named ‘Craig interpolation’ theorem established by Rauszer in [24] since that article is about the property more correctly named ‘deductive (...) interpolation’ (see Galatos, Jipsen, Kowalski and Ono’s use of this term in [5]) for global consequence. Given that the deduction theorem fails for bi-intuitionistic logic with global consequence, the two formulations of the property are not equivalent. (shrink)

Given some links between Lyndon’s Interpolation Theorem, term distribution, and Sommers and Englebretsen’s logic, in this contribution we attempt to capture a sense of interpolation for Sommers and Englebretsen’s Term Functor Logic. In order to reach this goal we first expound the basics of Term Functor Logic, together with a sense of term distribution, and then we offer a proof of our main contribution.

Continuing work initiated by Jónsson, Daigneault, Pigozzi and others; Maksimova proved that a normal modal logic (with a single unary modality) has the Craig interpolation property iff the corresponding class of algebras has the superamalgamation property (cf. [Mak 91], [Mak 79]). The aim of this paper is to extend the latter result to a large class of logics. We will prove that the characterization can be extended to all algebraizable logics containing Boolean fragment and having a certain kind of (...) local deduction property. We also extend this characterization of the interpolation property to arbitrary logics under the condition that their algebraic counterparts are discriminator varieties. We also extend Maksimova's result to normal multi-modal logics with arbitrarily many, not necessarily unary modalities, and to not necessarily normal multi-modal logics with modalities of ranks smaller than 2, too.The problem of extending the above characterization result to no n-normal non-unary modal logics remains open. (shrink)

Probabilism says an agent is rational only if her credences are probabilistic. This paper is concerned with the so-called Accuracy Dominance Argument for Probabilism. This argument begins with the claim that the sole fundamental source of epistemic value for a credence is its accuracy. It then shows that, however we measure accuracy, any non-probabilistic credences are accuracy-dominated: that is, there are alternative credences that are guaranteed to be more accurate than them. It follows that non-probabilistic credences (...) are irrational. In this paper, I identify and explore a lacuna in this argument. I grant that, if the only doxastic attitudes are credal attitudes, the argument succeeds. But many philosophers say that, alongside credences, there are other doxastic attitudes, such as full beliefs. What's more, those philosophers typically claim, these other doxastic attitudes are closely connected to credences, either as a matter of necessity or normatively. Now, since full beliefs are also doxastic attitudes, it seems that, like credences, the sole source of epistemic value for them is their accuracy. Thus, if we wish to measure the epistemic value of an agent's total doxastic state, we must include not only the accuracy of her credences, but also the accuracy of her full beliefs. However, if this is the case, there is a problem for the Accuracy Dominance Argument for Probabilism. For all the argument says, there might be non-probabilistic credences such that there is no total doxastic state that accuracy-dominates the total doxastic state to which those credences belong. (shrink)

Interpolation has become one of the standard properties that logicians investigate when designing a logic. In this paper, we provide strong evidence that the presence of interpolants is not only cogent for scientific reasoning but has also important practical implications in computer science. We illustrate that interpolation in general, and uniform splitting interpolants, in particular, play an important role in applications where formality and modularity are invoked. In recognition of the fact that common logical formalisms often lack uniform (...) interpolants, we advocate the need for developing general methods to engineer a specification logic so that some critical uniform interpolants become available. (shrink)

We provide a direct method for proving Craig interpolation for a range of modal and intuitionistic logics, including those containing a "converse" modality. We demonstrate this method for classical tense logic, its extensions with path axioms, and for bi-intuitionistic logic. These logics do not have straightforward formalisations in the traditional Gentzen-style sequent calculus, but have all been shown to have cut-free nested sequent calculi. The proof of the interpolation theorem uses these calculi and is purely syntactic, without resorting (...) to embeddings, semantic arguments, or interpreted connectives external to the underlying logical language. A novel feature of our proof includes an orthogonality condition for defining duality between interpolants. (shrink)

Suppose that beliefs come in degrees. How should we then measure the accuracy of these degrees of belief? Scoring rules are usually thought to be the mathematical tool appropriate for this job. But there are many scoring rules, which lead to different ordinal accuracy rankings. Recently, Fallis and Lewis [2016] have given an argument that, if sound, rules out many popular scoring rules, including the Brier score, as genuine measures of accuracy. I respond to this argument, in (...) part by noting that the argument fails to account for verisimilitude—that certain false hypotheses might be closer to the truth than other false hypotheses are. Oddie [forthcoming], however, has argued that no member of a very wide class of scoring rules (the so-called proper scores) can appropriately handle verisimilitude. I explain how to respond to Oddie's argument, and I recommend a class of weighted scoring rules that, I argue, genuinely measure accuracy while escaping the arguments of Fallis and Lewis as well as Oddie. (shrink)

Arrow and turnstile interpolations are investigated in UCL [introduced by Sernadas et al. ], a logic that is a complete extension of classical propositional logic for reasoning about connectives that only behave as expected with a given probability. Arrow interpolation is shown to hold in general and turnstile interpolation is established under some provisos.

We investigate interpolation properties of many-valued propositional logics related to continuous t-norms. In case of failure of interpolation, we characterize the minimal interpolating extensions of the languages. For finite-valued logics, we count the number of interpolating extensions by Fibonacci sequences.

The Craig interpolation property is investigated for substructural logics whose algebraic semantics are varieties of semilinear pointed commutative residuated lattices. It is shown that Craig interpolation fails for certain classes of these logics with weakening if the corresponding algebras are not idempotent. A complete characterization is then given of axiomatic extensions of the “R-mingle with unit” logic that have the Craig interpolation property. This latter characterization is obtained using a model-theoretic quantifier elimination strategy to determine the varieties (...) of Sugihara monoids admitting the amalgamation property. (shrink)

Credences, unlike full beliefs, can’t be true or false. So what makes credences more or less accurate? This chapter offers a new answer to this question: credences are accurate insofar as they license true educated guesses, and less accurate insofar as they license false educated guesses. This account is compatible with immodesty; : a rational agent will regard her own credences to be best for the purposes of making true educated guesses. The guessing account can also be used to justify (...) certain coherence constraints on rational credence, such as probabilism. The chapter concludes by discussing some advantages of the guessing account over rival accounts of accuracy. (shrink)

The provability logic GL was in the field of interest of A.V. Kuznetsov, who had also formulated its intuitionistic analog—the intuitionisticprovability logic—and investigated these two logics and their extensions.In the present paper, different versions of interpolation and of the Bethproperty in normal extensions of the provability logic GL are considered. Itis proved that in a large class of extensions of GL almost all versions of interpolation and of the Beth propertyare equivalent. It follows that in finite slice logics (...) over GL the three versionsCIP, IPD and IPR of the interpolation property are equivalent. Also theyare equivalent to the Beth properties B1, PB1 and PB2. (shrink)

This chapter examines global policing as it takes shape through the work of Interpol, the International Criminal Police Organization. Global policing emerges in the legal, political and technological amalgam through which transnational police cooperation is carried out, and includes the police practices inflected and made possible by this phenomenon. Interpol’s role is predominantly in the circulation of information, through which it enters into relationships and provides services that affect aspects of governance, from the local to national, regional and global. The (...) chapter describes this assemblage as a noteworthy experiment in developing what McKeon called a frame for common action. Drawing on Interpol publications, news stories, interviews with staff, and fieldwork at the General Secretariat in Lyon, France, the history, institutional structure, and daily practices are described. Three cases are analyzed, concerning Red Notices, national sovereignty, and terrorism, in order to explore some of the problems arising in Interpol’s political and technical operating arrangements. In conclusion, international and global policing are compared schematically, together with Interpol’s attempts to give institutional and procedural direction to the still-evolving form of global policing. (shrink)

In a recent paper we have defined an analytic tableau calculus PL_16 for a functionally complete extension of Shramko and Wansing's logic based on the trilattice SIXTEEN_3. This calculus makes it possible to define syntactic entailment relations that capture central semantic relations of the logic---such as the relations |=_t, |=_f, and |=_i that each correspond to a lattice order in SIXTEEN_3; and |=, the intersection of |=_t and |=_f,. -/- It turns out that our method of characterising these semantic relations---as (...) intersections of auxiliary relations that can be captured with the help of a single calculus---lends itself well to proving interpolation. All entailment relations just mentioned have the interpolation property, not only when they are defined with respect to a functionally complete language, but also in a range of cases where less expressive languages are considered. For example, we will show that |=, when restricted to L_{tf}, the language originally considered by Shramko and Wansing, enjoys interpolation. This answers a question that was recently posed by M. Takano. (shrink)

A semantical definition of abstract logics is given. It is shown that the Craig interpolation property implies the Beth definability property, and that the Souslin-Kleene interpolation property implies the weak Beth definability property. An example is given, showing that Beth does not imply Souslin-Kleene.

Craig's interpolation lemma (if φ → ψ is valid, then φ → θ and θ → ψ are valid, for θ a formula constructed using only primitive symbols which occur both in φ and ψ) fails for many propositional and first order modal logics. The interpolation property is often regarded as a sign of well-matched syntax and semantics. Hybrid logicians claim that modal logic is missing important syntactic machinery, namely tools for referring to worlds, and that adding such (...) machinery solves many technical problems. The paper presents strong evidence for this claim by defining interpolation algorithms for both propositional and first order hybrid logic. These algorithms produce interpolants for the hybrid logic of every elementary class of frames satisfying the property that a frame is in the class if and only if all its point-generated subframes are in the class. In addition, on the class of all frames, the basic algorithm is conservative: on purely modal input it computes interpolants in which the hybrid syntactic machinery does not occur. (shrink)

By a consequence relation on a set L of formulas we understand a relation I — c p(L) x L satisfying the conditions called 'Overlap', 'Dilution', and 'Cut for Sets' at p.15 of [25]; we do not repeat the conditions here since we are simply fixing notation and the concept of a consequence relation is well known in any case. (The characterization in [25] amounts to that familiar from Tarski's work, except that there is no 'finitariness' restriction to the effect (...) that when I I — A, for I c L, A c L, we must have I o I — A for some finite I o c I . The presence or absence of this condition makes no difference to anything that follows.) Each language L to be considered will be a sentential language whose formulas are built in the usual way by application of it-ary (primitive) connectives to it simpler formulas, starting with the simplest formulas — the propositional variables (or 'sentence letters') — not constructed with the aid of connectives. We assume, as usual, that there are countably many such variables, and they will be denoted by p, q, r, ... possibly with numerical subscripts. A consequence relation I- on such an L has the Unrestricted Interpolation Property when for any A, C c L with A I — C, there exists B c L with A I — B and B I — C, such that C is constructed only out of such propositional variables as occur both in A and in C. (Such a B is called an interpolant for A and C.) Note that we take the usual notational liberties here, writing "A I — C" (and the like) for "iAi I — C", "I, A I — C" to mean "I u iAi I — C", and "I — C" to mean "8 I — C". Further, we sometimes abbreviate the claim that A I — B and B I — C to "A I — B I — C", and when C is A itself, we always write this simply as "A — II— B".. (shrink)

Important positive as well as negative results on interpolation property in fragments of the intuitionistic propositional logic (INT) were obtained by J. I. Zucker in [6]. He proved that the interpolation theorem holds in purely implicational fragment of INT. He also gave an example of a fragment of INT for which interpolation fails. This fragment is determined by the constant falsum (), well known connectives: implication () and conjunction (), and by a ternary connective defined as follows: (...) (p, q, r)= df (pq)(pr).Extending this result of J. I. Zucker, G. R. Renardel de Lavalette proved in [5] that there are continuously many fragments of INT without the interpolation property. (shrink)

Accuracy arguments for the core tenets of Bayesian epistemology differ mainly in the conditions they place on the legitimate ways of measuring the inaccuracy of our credences. The best existing arguments rely on three conditions: Continuity, Additivity, and Strict Propriety. In this paper, I show how to strengthen the arguments based on these conditions by showing that the central mathematical theorem on which each depends goes through without assuming Additivity.

This paper challenges “traditional measurement-accuracy realism”, according to which there are in nature quantities of which concrete systems have definite values. An accurate measurement outcome is one that is close to the value for the quantity measured. For a measurement of the temperature of some water to be accurate in this sense requires that there be this temperature. But there isn’t. Not because there are no quantities “out there in nature” but because the term ‘the temperature of this water’ (...) fails to refer owing to idealization and failure of specificity in picking out concrete cases. The problems can be seen as an artifact of vagueness, and so doing facilitates applying Eran Tal’s robustness account of measurement accuracy to suggest an attractive way of understanding vagueness in terms of the function of idealization, a way that sidesteps the problems of higher order vagueness and that shows how idealization provides a natural generalization of what it is to be vague. (shrink)

The splitting theorem says that any set of formulae has a finest representation as a family of letter-disjoint sets. Parikh formulated this for classical propositional logic, proved it in the finite case, used it to formulate a criterion for relevance in belief change, and showed that AGMpartial meet revision can fail the criterion. In this paper we make three further contributions. We begin by establishing a new version of the well-known interpolation theorem, which we call parallel interpolation, use (...) it to prove the splitting theorem in the infinite case, and show how AGM belief change operations may be modified, if desired, so as to ensure satisfaction of Parikh’s relevance criterion. (shrink)

In Bayesian epistemology, the problem of the priors is this: How should we set our credences (or degrees of belief) in the absence of evidence? That is, how should we set our prior or initial credences, the credences with which we begin our credal life? David Lewis liked to call an agent at the beginning of her credal journey a superbaby. The problem of the priors asks for the norms that govern these superbabies. -/- The Principle of Indifference gives a (...) very restrictive answer. It demands that such an agent divide her credences equally over all possibilities. That is, according to the Principle of Indifference, only one initial credence function is permissible, namely, the uniform distribution. In this paper, we offer a novel argument for the Principle of Indifference. I call it the Argument from Accuracy. (shrink)

In this paper we will be concerned with the interpretability logic of PA and in particular with the fact that this logic, which is denoted by ILM, does not have the interpolation property. An example for this fact seems to emerge from the fact that ILM cannot express Σ₁-ness. This suggests a way to extend the expressive power of interpretability logic, namely, by an additional operator for Σ₁-ness, which might give us a logic with the interpolation property. We (...) will formulate this extension, give an axiomatization which is modally complete and arithmetically complete (although for proofs of these theorems we refer to an earlier paper), and investigate interpolation. We show that this logic still does not have the interpolation property. (shrink)

The semantic valuations of classical logic, strong Kleene logic, the logic of paradox and the logic of first-degree entailment, all respect the Dunn conditions: we call them Dunn logics. In this paper, we study the interpolation properties of the Dunn logics and extensions of these logics to more expressive languages. We do so by relying on the \ calculus, a signed tableau calculus whose rules mirror the Dunn conditions syntactically and which characterizes the Dunn logics in a uniform way. (...) In terms of the \ calculus, we first introduce two different interpolation methods, each of which uniformly shows that the Dunn logics have the interpolation property. One of the methods is closely related to Maehara’s method but the other method, which we call the pruned tableau method, is novel to this paper. We provide various reasons to prefer the pruned tableau method to the Maehara-style method. We then turn our attention to extensions of Dunn logics with so-called appropriate implication connectives. Although these logics have been considered at various places in the literature, a study of the interpolation properties of these logics is lacking. We use the pruned tableau method to uniformly show that these extended Dunn logics have the interpolation property and explain that the same result cannot be obtained via the Maehara-style method. Finally, we show how the pruned tableau method constructs interpolants for functionally complete extensions of the Dunn logics. (shrink)

An interpolation Theorem is proved for first order logic with infinitary predicates. Our proof is algebraic via cylindric algebras.1.