The measure of risk aversion
... We will say that u is a linear function on a mixture set M if it is a real-valued function for which u(λx⊕(1−λ)y) = λu(x)+(1−λ)u(y) for all λ and x, y ∈ M . Two linear functions u and v are related by a positive affine transformation if there are real numbers a > 0 and b such that v(x) = au(x) + b f ...
... We will say that u is a linear function on a mixture set M if it is a real-valued function for which u(λx⊕(1−λ)y) = λu(x)+(1−λ)u(y) for all λ and x, y ∈ M . Two linear functions u and v are related by a positive affine transformation if there are real numbers a > 0 and b such that v(x) = au(x) + b f ...
pse14 VanLong 19108260 en
... one has to decipher the necessary conditions for a differential equation to have a (unique) solution, a question about which little is known without imposing more structure. Sufficient conditions are easier to explore9 , but are of course more restrictive than one would like, in particular those requir ...
... one has to decipher the necessary conditions for a differential equation to have a (unique) solution, a question about which little is known without imposing more structure. Sufficient conditions are easier to explore9 , but are of course more restrictive than one would like, in particular those requir ...
Category Theory Lecture Notes for ESSLLI Michael Barr Department
... The significance of the fact that the composite c is defined on G2 is that g ◦ f is defined if and only if the source of g is the target of f . This means that composition is a function whose domain is an equationally defined subset of G1 × G1 : the equation requires that the source of g equal the t ...
... The significance of the fact that the composite c is defined on G2 is that g ◦ f is defined if and only if the source of g is the target of f . This means that composition is a function whose domain is an equationally defined subset of G1 × G1 : the equation requires that the source of g equal the t ...
Lecture 04: Risk Preferences and Risk Preferences and Expected
... A preference ordering is (i) complete, (ii) transitive, (iii) continuous and [(iv) relatively stable] can be represented by a utility function, i.e. (c0,cc1,…,ccS) Â (c (c’0,cc’1,…,cc’S) ⇔ U(c0,c1,…,cS) > U(c’0,c’1,…,c’S) (preference ordering over lotteries – (S+1)-dimensional (S ...
... A preference ordering is (i) complete, (ii) transitive, (iii) continuous and [(iv) relatively stable] can be represented by a utility function, i.e. (c0,cc1,…,ccS) Â (c (c’0,cc’1,…,cc’S) ⇔ U(c0,c1,…,cS) > U(c’0,c’1,…,c’S) (preference ordering over lotteries – (S+1)-dimensional (S ...
A Course in Modal Logic - Sun Yat
... concepts, whereas these differences are actually supported by different intuitive semantics (even philosophical background). The reader who is interested in this can refer to the related literature. (Ⅱ) The cardinality of At is finite or countable infinite, but, in fact, most of results given in thi ...
... concepts, whereas these differences are actually supported by different intuitive semantics (even philosophical background). The reader who is interested in this can refer to the related literature. (Ⅱ) The cardinality of At is finite or countable infinite, but, in fact, most of results given in thi ...
Harmony, Normality and Stability
... Dummett singles out two features of the use of expressions that are of central importance for specifying their meanings. The two features are intended to apply very generally to all kinds of expressions, but I’m only concerned with the logical constants. ‘The first category [of principles governing ...
... Dummett singles out two features of the use of expressions that are of central importance for specifying their meanings. The two features are intended to apply very generally to all kinds of expressions, but I’m only concerned with the logical constants. ‘The first category [of principles governing ...
Social Preferences, Beliefs, and the Dynamics of Free Riding in
... cooperation” is an interesting candidate for explaining the fragility of cooperation because this motivation depends directly on how others behave or are believed to behave. Conditional cooperators who observe (or believe) that others free ride, will reduce their contributions and thus contribute to ...
... cooperation” is an interesting candidate for explaining the fragility of cooperation because this motivation depends directly on how others behave or are believed to behave. Conditional cooperators who observe (or believe) that others free ride, will reduce their contributions and thus contribute to ...
The Z/EVES 2.0 User`s Guide - Department of Computer Science
... of order; if such a specification is imported into Z/EVES it is necessary to move the paragraphs into a suitable checking order. Order is also important for theorems, as the proof of a given theorem can only use other theorems that precede the given theorem in the specification. Thus, lemmas must ap ...
... of order; if such a specification is imported into Z/EVES it is necessary to move the paragraphs into a suitable checking order. Order is also important for theorems, as the proof of a given theorem can only use other theorems that precede the given theorem in the specification. Thus, lemmas must ap ...
Introduction to Linear Programming
... A dictionary is completely determined by specifying B and N ...
... A dictionary is completely determined by specifying B and N ...
Random Expected Utility,
... identical characteristics each facing the same decision problem presents the observer with a frequency distribution over outcomes. Typically, such data is interpreted as the outcome of independent random choice by a group of identical individuals. Even when repeated decisions of a single individual ...
... identical characteristics each facing the same decision problem presents the observer with a frequency distribution over outcomes. Typically, such data is interpreted as the outcome of independent random choice by a group of identical individuals. Even when repeated decisions of a single individual ...
Marginal Utility Theory of Household Behavior
... Or, the household consumes enough of each commodity so that the marginal utility per dollar of the last unit consumed is equal for all goods consumed. <> The
household could increase its welfare by reallocating consumption
away from the low ratio ...
... Or, the household consumes enough of each commodity so that the marginal utility per dollar of the last unit consumed is equal for all goods consumed. <
A survey on Interactive Theorem Proving
... The history of mathematics has stories about false results that went undetected for long periods of time. However, it is generally believed that if a published mathematical argument is not valid, it will be eventually detected as such. While the process of finding a proof may require creative insigh ...
... The history of mathematics has stories about false results that went undetected for long periods of time. However, it is generally believed that if a published mathematical argument is not valid, it will be eventually detected as such. While the process of finding a proof may require creative insigh ...
Proof-Net Categories - Matematički Institut SANU
... definitions, and also for motivation from the perspective of general proof theory or categorial proof theory. At some key points, we rely on results proved before. In Chapter 2 we rely on matters proved in [20], [21] and [22], and in particular on a coherence result from [22] (Symmetric Net Coherenc ...
... definitions, and also for motivation from the perspective of general proof theory or categorial proof theory. At some key points, we rely on results proved before. In Chapter 2 we rely on matters proved in [20], [21] and [22], and in particular on a coherence result from [22] (Symmetric Net Coherenc ...
Proof-Net Categories - Matematički Institut SANU
... categories. This result involves a proviso concerning the units, but does not exclude them completely (as we announced in the preceding section). This coherence of star-autonomous categories is a powerful tool for verifying whether a diagram of arrows commutes in star-autonomous categories. After al ...
... categories. This result involves a proviso concerning the units, but does not exclude them completely (as we announced in the preceding section). This coherence of star-autonomous categories is a powerful tool for verifying whether a diagram of arrows commutes in star-autonomous categories. After al ...
Henkin`s Method and the Completeness Theorem
... In addition to formal manipulation of the formulas of this system we shall be concerned with their meaning according to the following interpretation. The propositional constants are to denote one of the truth values, T or F, the symbol “f ” denoting F, and the propositional variables are to have the ...
... In addition to formal manipulation of the formulas of this system we shall be concerned with their meaning according to the following interpretation. The propositional constants are to denote one of the truth values, T or F, the symbol “f ” denoting F, and the propositional variables are to have the ...
Everything Else Being Equal: A Modal Logic for Ceteris Paribus
... modally equivalent, written M, w M , v, iff they satisfy exactly the same formulas of LP . Definition 4 (Bisimulation) Two pointed models M, w and M , v are bisimilar (written M, w ↔ M , v) iff there is a relation E ⊆ M × M such that, for all states s ∈ M and t ∈ M : 1. If sEt then for all p ...
... modally equivalent, written M, w M , v, iff they satisfy exactly the same formulas of LP . Definition 4 (Bisimulation) Two pointed models M, w and M , v are bisimilar (written M, w ↔ M , v) iff there is a relation E ⊆ M × M such that, for all states s ∈ M and t ∈ M : 1. If sEt then for all p ...
1- ISSN 1045-6333 NOTIONS OF FAIRNESS
... reader to contemplate the converse: suppose that no matter how much the degree of fairness differed between two regimes, a notion of fairness never implied that one regime was superior to another when all else was equal, namely, when everyone had the same level of well-being. Clearly, there is no se ...
... reader to contemplate the converse: suppose that no matter how much the degree of fairness differed between two regimes, a notion of fairness never implied that one regime was superior to another when all else was equal, namely, when everyone had the same level of well-being. Clearly, there is no se ...
Barwise: Infinitary Logic and Admissible Sets
... become isomorphic if the set-theoretic world were extended in such a way as to collapse the cardinalities of both structures to ℵ0 . There is one special case where potential isomorphism does imply isomorphism. Using Cantor’s original argument, one can show that any two countable structures which ar ...
... become isomorphic if the set-theoretic world were extended in such a way as to collapse the cardinalities of both structures to ℵ0 . There is one special case where potential isomorphism does imply isomorphism. Using Cantor’s original argument, one can show that any two countable structures which ar ...
Expected Uncertain Utility Theory,
... prior of B. Hence, both decision makers perceive the same range of uncertainty. (ii) Two decision makers have the same uncertainty attitude (the same von NeumannMorgenstern index) if and only if 1’s certainty equivalent of the bet yAx is the same as 2’s uncertainty equivalent of the bet yBx for all ...
... prior of B. Hence, both decision makers perceive the same range of uncertainty. (ii) Two decision makers have the same uncertainty attitude (the same von NeumannMorgenstern index) if and only if 1’s certainty equivalent of the bet yAx is the same as 2’s uncertainty equivalent of the bet yBx for all ...
Combining Paraconsistent Logic with Argumentation
... moreover, allow for the full reasoning power of a deductive logic. Although for many cases less expressiveness may suffice, a full theory of the logic of argumentation cannot exclude the general case. Caminada, Carnielli and Dunne [5] formulated a new set of rationality postulates in addition to tho ...
... moreover, allow for the full reasoning power of a deductive logic. Although for many cases less expressiveness may suffice, a full theory of the logic of argumentation cannot exclude the general case. Caminada, Carnielli and Dunne [5] formulated a new set of rationality postulates in addition to tho ...