In addition, I judge quite extreme Adams suggestion because it is not complicate to find in natural language several examples of **conditional** **sentences** considered true or false by our common sense. Edgington herself admitted--during a seminar at University of Sassari--that sometimes a **conditional** could have a **truth**- value. However, although she looked less radical than Adams, she refused to talk in terms of general **truth** **conditions**. After all, the fact that we are not always able to assign a **truth**-value is unquestionable. Even Stalnaker had to admit--especially after Lewis objections--that sometimes we cannot choose the possible world closest to the actual one and, consequently, the **conditional** is neither true nor false--reason for what he dealt with Van Fraassen s supervaluations.

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As argued in the previous section, we assume that the thematic topic WA and GA for neutral descriptions do not induce the application of Existential Introduction to generate alternative sets (or which are taken to be invisible because they are irrelevant for **truth**-**conditional** meanings of **sentences**). On the other hand, the focalized subject marked with the exaustive listing GA elicits a set of alternatives (or make it relevant and visible for the interpretation). Actually, this is not limited to the nominative subject. Since any noun phrase or postpositional phrase must provide an exhaustive list of referents if it is focalized, the following derivation should hold for any focus phrase. Again, maintaining the radical lexicalist approach, we pack all the meaning necessary to induce exhaustiveness to the focalized GA, as follows:

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Given that I've argued (hopefully convincingly) that sentences aren't the kind of entity that can be given truth conditions, a linguistic expression could be said to have 'truth-conditio[r]

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We assume that to found a particle in a particular state is a probabilistic phenome- non for which we have join **probability** that the particle can be in a particular state. Now the novelty is to assume that the **probability** is function of other external elements as parameters. The average of the position for the particle is a parameter the movement of the particle in a particular environment for example inside of a tube or in other boundary condition (see boundary condition in Shrodinger solution) can change the **probability** for a particular state. Any far or near change of the environment change the **probability** of the state (Bell theorem and entanglement) In conclusion the join proba- bility of a state of different variables is conditioned by a set of parameters that statically or physically can define the environment where the particle move. We denote all this parameters as the information relate to the environment where the particle is located. The set of external parameters is the information space that can have curvature as in the Berry phase phenomena that show that in the Shrodinger solution any loop can change the original phase. In differential geometry any loop in a space with curvature changes the original phase of the vectors. Now we built the information space which geodesic tensor is the Fisher entropy or Fisher information by which we can compute the covariant derivatives and the curvature.

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Suppose action a was in fact taken. If a, b are distinguishable for me, in the black dot on the left-hand side, I know exactly where I am through observation – though there is some 'ancient history' that with **probability** 1/2, b might have been taken. But if a, b are indistinguishable for me, on the right, I do not know what happened, and the earlier **probability** induces a live option that I am in the white world below. Here is another point which we can see in the Monty tree. First, one action type can have different probabilities at different nodes of the current tree level. E.g., 'opening door 2' has **probability** 1/2 when the car is behind door 1, but **probability** 1 with the car behind door 3. Of course, by making descriptions of action tokens disjoint, we can make probabilities unique – but this seems less natural in practice. Now for the product update rule along a branch. The usual textbook explanation makes **probability** of a branch a product of the probabilities of its actions. Recursively, this amounts to repeating the following step:

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In recent years, with the deeply study of model checking techniques, approximate and effective model checking on multiple until formulae (k>2) become an open research problem and more and more importance in the field of system biology. One of the typical applications is observe oscillatory behavior of CTMC model [9]. Literature [10] gives the detailed description of property verification method on time constraints multiple until formulae, and gives the algorithm description on stratified continuous time Markov chain model. The k-shortest(hop-constrained) paths algorithms for counterexample generation of until formulae reachability **probability** in discrete time Markov chains and a simple algorithm used to generate minimal regular expressions [11] of counterexample paths were both proposed in literature [12]. Literature [13] proposes a counterexample generation algorithm for model checking probabilistic timed automata based on the weighted directed graph. In the literature [14], the semantic representation of the probabilistic timed automata was gave by Markov decision process, and the until formulae counterexample generation algorithm was proposed. In summary, the research on the issue of counterexample mainly focused on the basic probabilistic model and the time constraint until formulae properties.

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A pioneering result with far-reaching consequences in quantum information and communication theory is the no-cloning theorem, stating that unknown pure quan- tum states cannot be copied unless they are orthogo- nal [12, 29–31]. An interesting generalization is the no- broadcasting theorem for mixed states [3]. Originally, both were proved in Hilbert space quantum mechanics, then extended to the C*-algebraic setting [11] and later to finite-dimensional generic probabilistic models [1, 2] and to quantum logics [20]. In the latter case, only uni- versal cloning is impossible, while the cloning of a small set or pair of states can be ruled out in the other cases. Though these results preclude the perfect cloning, the approximate or imperfect cloning of quantum states re- mains possible [8, 10, 19]. In this paper, the (perfect) cloning of a small set or pair of states is considered in the setting of quantum logics with a **conditional** prob- ability calculus [21, 22], including finite-dimensional as well as infinite-dimensional models.

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We now turn to an evaluation of the fit of **truth** tables in Table 1 for the indicative conditionals. As said, we will allow the models to predict that the expected responses constitute at least a relative majority (a very lenient requirement). The results reported in Table 6 show that none of the models was able to accurately characterize the individuals’ responses. Overall, the modal responses indicate a slight tendency to judge indicative conditionals as true whenever the antecedent and the consequent have the same **truth** status (in accordance with the **truth** table of the material bi-**conditional**, which is true in the ⊤⊤ and ⊥⊥ cells and false otherwise ). This pattern is corroborated by the set of studies gathered by Schroyens (2010), which involved abstract stimulus materials with explicit negations and the option to respond that the **truth** table cell is ‘irrelevant’ for the **truth** value of the **conditional** (see Table 7).

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The figure shows that both the histogram estimator and the (**conditional**) kernel estimator reflect the two peaks in the true **conditional** density function quite accurately—as a unimodal estimator, the normal estimator is obviously not able to do so. However, a visual comparison of the estimates to the true **conditional** density shows that they do not model the height of the two peaks perfectly: they should be of the same height. This is due to the influence of discretization: the histogram estimate shows that the first peak is represented by two bars (corresponding to two discretization intervals) that together cover a wider range of target values than the single bar corresponding to the second peak. Thus the predicted class **probability** is spread across a wider range of target values and the height of the peak is reduced.

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In Lewis’s example there seems to be an implicit claim that there is no **conditional** or causal link between studying and flunking, or between not studying and flunking. Hence the studying and flunking are stated to be probabilistically independent. Such constructions are best understood as denials of a **conditional** relation between antecedent and consequent. A better formulation would be ‘Even if I study, I’ll still flunk’ or ‘It is not the case that if I study, I’ll pass’. We should think of such statements as ‘contra-conditionals’, as they are characteristically used to deny that the antecedent is a sufficient or even relevant condition for an expected consequent. Contra-conditionals do not allow contraposition, modus ponens or modus tollens, and would therefore not be suitable candidates for indicative or causal conditionals. If Adams’ Thesis fits such **conditional** constructions, we could take this as an indication of a logical discrepancy between the ratio analysis and **conditional** credence.

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Now the question arises: what is the reason that interac- tion does not occur in every case. That is due to the atomic vibrations or by other words the temperature of the particle. As a consequence of this relationship, it can be stated: in the case of photon generation the percentage of radiative elec- tron transitions is higher when the temperature is lower. Similarly, when photons are dissipated in a direct band gap semiconductor material the percentage of generating charge carriers is higher when the temperature is lower – assuming the same **conditions** (same number of photons, etc.) That is in good agreement with the experimental results [19].

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A seawall is an important form of coastal defence constructed on the inland part of a coast to reduce storm tide disasters and to defend the coast around a town or harbour from erosion. Generally, the design standard of a seawall is defined as the disasters protecting ability and may be expressed by the return period of design occurrence of storm tide disasters. The choice of the recommended return period in a region is usually made balancing the total costs of the seawall structure and the good benefit of coastal defence, and so the specified return period for the design of a seawall depends on economy, society and natural environment. This means a specified risk level of overtopping or damage of a seawall structure is usually allowed. The determination of the required seawall height is usually based on the combination of wind speed (or wave height) and water level according to the above-mentioned return period. To fully know the combined effect of both variables which influence the engineering design is a major advantage in incorporating the dependence between the two variables in design of a seawall. With a specified risk level allowed, the aim of this work is to define a methodology to identify the optimal combination between these two values for the design of seawalls based on **conditional** risk **probability**.

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In the last month, the situation has deteriorated dramatically. First-time buyers have generally not been in the market for some considerable time, thereby causing structural issues and preventing chains forming. Estate agents with whom I have spoken over the last few weeks are, bluntly, “scared witless”. They have finally accepted that adjustments to asking prices are warranted in current market **conditions** and have talked to their vendors, negotiating price reductions, but nothing is happening. A very well respected and successful estate agent I have known for many years was selling between 20 and 25 houses per calendar month last summer. They are now selling an average of 2 houses per calendar month and are seeing increasing numbers of applicants pulling out or vendors withdrawing their properties from the market.

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It is easy to cook up an example along the lines of 3.1 which satisfies the second condition. It follows that we cannot simply take the domain of a **conditional** quantifier to be the Borel σ-algebra generated by τ. This is somewhat out of keeping with our general aim of using a logic which is as simple as possible to describe the resource. Below we shall tackle this problem in two ways. In the next section, we show that at least as far as completeness is concerned, the complexity of the denotation of conditionally quantified formulas can be kept small; this is achieved by resorting to a type of nonstandard model first introduced by Harvey Friedman, the so called Borel models. We then move on to slightly change the logical properties of the **conditional** quantifier, dropping the property that ϕ ≤ ∃ (ϕ |G ), and show that it has the effect of lowering complexity of denotation. In this case the Borel σ-algebra suffices as a domain of the quantifier. **Conditional** quantifiers will make a further appearance in section 9, where they will be used to provide simple examples of interesting families of quantifiers, martingales.

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In this paper, we consider coherent imprecise **probability** assessments on ®nite families of **conditional** events and we study the problem of their extension. With this aim, we adopt a generalized de®nition of coherence, called g-coherence, which is based on a suitable generalization of the coherence principle of de Finetti. At ®rst, we recall some theoretical results and an algorithm obtained in some previous papers where the case of precise **conditional** **probability** assessments has been studied. Then, we extend these results to the case of imprecise probabilistic assessments and we obtain a theorem which can be looked at as a generalization of the version of the fundamental theorem of de Finetti given by some authors for the case of **conditional** events. Our algorithm can also be exploited to produce lower and upper probabilities which are coherent in the sense of Walley and Williams. Moreover, we compare our approach to similar ones, like **probability** logic or probabilistic deduction. Finally, we apply our algorithm to some well-known inference rules assuming some logical relations among the given events. Ó 2000 Elsevier Science Inc. All rights reserved.

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Analysis of multiple noninvasive tests offers the promise of more accurate diagnosis of coronary artery disease, but discordant test responses can occur frequently and, when observed, result in diagnostic uncertainty. Accordingly, 43 patients undergoing diagnostic coronary angiography were evaluated by noninvasive testing and the results subjected to analysis using Bayes' theorem of **conditional** **probability**. The procedures used included electrocardiographic stress testing for detection of exercise-induced ST segment

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There is a definite need for representations of and tools for **conditional** **probability** that enhance understanding, simplify calculations, foster insight, and facilitate reasoning. Such representations and tools are useful in a wide variety of disciplines, but their utility in medical contexts and applications are stressed herein, so as to address a clinical rather than a mathematical audience. We employ a plethora of time-tested pedagogical representations or tools of **conditional** **probability** including: (a) Visualization on Venn diagrams or Karnaugh maps, (b) Reformulation as natural frequencies, (c) Entity interrelations via Signal Flow Graphs, as (d) Specification of certain problem formats such as the format of Trinomial Graphs. The new representations or tools have well known histories of pedagogical advantages, but are still to be tested in the specific realm of **conditional** **probability**. Further assessment of the novel representations or tools proposed herein is needed. Each of these is to be taught to a group of students, and a control group of students is to be

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In scientific literature, **sentences** that cite re- lated work can be a valuable resource for applications such as summarization, syn- onym identification, and entity extraction. In order to determine which equivalent en- tities are discussed in the various citation **sentences**, we propose aligning the words within these **sentences** according to semantic similarity. This problem is partly analogous to the problem of multiple sequence align- ment in the biosciences, and is also closely related to the word alignment problem in sta- tistical machine translation. In this paper we address the problem of multiple citation concept alignment by combining and mod- ifying the CRF based pairwise word align- ment system of Blunsom & Cohn (2006) and a posterior decoding based multiple se- quence alignment algorithm of Schwartz & Pachter (2007). We evaluate the algorithm on hand-labeled data, achieving results that improve on a baseline.

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Leitgeb develops his theory and provides all these results in a classical **probability** setting (Kolmogorov’s axioms). However, this setting is too restrictive. This is because in a classical **probability** setting conditioning on events with measure 0 is not defined. Suppose for example that we have a space W and A, B ⊆ W such that P (A) = 0. Then P (B|A) = P (A∩B) P(A) , a fraction that is not defined since the denominator is 0. Now this restriction poses an issue in belief revision, since as Halpern writes “That makes it unclear how to proceed if an agent learns something to which she initially assigned **probability** 0” ([29]). Hence when an agent is confronted with the occurrence of an event she considered impossible, instead of revising her beliefs she would raise her hands in despair. As Baltag and Smets write “it is well known that simple (classical) **probability** measures yield problems in the context of describing an agent’s beliefs and how they can be revised”([8, p. 3]). Although consideration of events with measure 0 might seem to be of little interest, Halpern argues ([29, pp.1,2]) that it plays an essential role in game theory, “particularly in the analysis of strategic reasoning in extensive form games and in the analysis of weak dominance in normal form games”. See for example (among others) [12], [13], [20], [16], [17], [31], [30]. Moreover, conditioning on events with measure 0 is also crucial in the analysis of **conditional** statements in philosophy ([1], [37]) and in dealing with monotonicity in AI ([33]). One way of preempting this problem without giving up classical **probability** is to demand that only impossible events can have **probability** 0. However, this entails that agents never have any wrong beliefs about anything, which seems to be a rather severe constraint. Hence Baltag and Smets’ conclusion that classical probabilities can not deal with any non-trivial belief revision ([8, p. 3]) seems indeed correct. And this is the main idea that motivates this thesis: to provide an extension of Leitgeb’s theory into non-classical **probability** spaces.

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