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Showing 1 to 15 of 15 for “"Axiomatization"”.
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Axiomatization and Incompleteness in Arithmetic and Set Theory
Axiomatization and Incompleteness in Arithmetic and Set Theory Wesley Duncan Wrigley I argue that are (at least) two distinct kinds of mathematical incompleteness. Part A of the thesis discusses Gödelian incompleteness, while Part B is concerned with set-theoretic incompleteness. Both parts are …
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Varieties and Clones of Relational Structures
We present an axiomatization of relational varieties, i.e., classes of relational structures closed under formation of products and retracts, by a certain class of first-order sentences. We apply this result to categorically equivalent algebras and primal algebras. We consider the relational …
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Taming the impossible
… closer attention. In chapter 4, I provide an axiomatization of a propositional fragment of the model theory developed in chapter 3 and prove that the axiomatization is complete and that the resulting conditional logic is decidable. This logic display some surprising features. While validating …
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Essays in Economic Theory
… concern. The second chapter offers an axiomatization of risk models where the choices of the decision maker are correlation sensitive. By extending the techniques of conjoint measurement to the nondeterministic case, we show that transitivity is the vN-M axiom that has to be relaxed to …
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Unilinear Residuated Lattices
… lattices. By presenting the constructions and axiomatizations for different classes of unilinear residuated lattices, we conclude that the study of unilinear residuated lattices can be reduced to the study of the ⊤-unital ones. Using the classification of unilinear residuated lattices, the …
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An essay in natural modal logic
… this very general setting, I provide the first axiomatization of the dyadic modal logic corresponding to the class of all g.i. frames. Various correspondences between dyadic logics and first order definable subclasses of the class of g.i. frames are established. Finally, some general model …
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Problems in the Theory of Convergence Spaces
… sequences. Fourth, we show that a standard axiomatization of mereology is equivalent to the condition that a topological space is discrete, and consequently, any model of general extensional mereology is indistinguishable from a model of set theory; we then generalize these results to the …
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New non-additive integrals in Multiple Criteria Decision Analysis
The proposal and the axiomatization of new fuzzy integrals has a central role in modern Multiple Criteria Decision Analysis. In this thesis we propose some generalizations of well known fuzzy integrals (Choquet, Shilkret and Sugeno). We propose and characterize bipolar fuzzy integrals, which are …
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Grothendieck Semirings and Definable Endofunctions
… is axiomatizable, and we use an explicit axiomatization to build a non-pseudofinite vector space. Other results include: extension of an Euler characteristic to interpretable sets; construction of translation-invariant measures on lattices generated by cosets of subgroups; said property of …
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Zariski structures and simple theories
… Zariski structure context, I consider Zilber's axiomatization in stable examples, and then in the case of the simple theory given by an algebraically closed field with a generic predicate. Comparing Zariski structure methods with corresponding techniques in algebraic geometry, I show the notions …
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The formal relationship between direct and continuation-passing style optimizing compilers: A synthesis of two paradigms
… effects, a sound and complete equational axiomatization of the semantics of call-by-value control operators, a methodology for deriving equational logics for imperative languages, and formal relationships between code generators and data flow analyzers for direct and CPS compilers. These …
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The Theory of Exponential Differential Equations
… of a set of differential equations and give an axiomatization for the theory of the exponential differential equations of split semiabelian varieties. In particular, this includes the theory of the equations satisfied by the usual complex exponential function and the Weierstrass p-functions. The …
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Fundamentals and applications of order dependencies
… the following: (i) a sound and complete axiomatization for UODs which is sound for ODs; (ii) a hierarchy of order dependency classes; (iii) a proof of co-NP-completeness of the inference problem for ODs and for the subclass of UODs; (iv) a proof of co-NP-completeness of the inference …
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Cost Sharing Models in Game Theory = Költségelosztási modellek a játékelméletben
… of Dubey (1982) and Moulin and Shenker (1992) on axiomatization of the Shapley value on the class of airport games to the class of irrigation games. We have \translated" the axioms used in cost allocation literature to the axioms corresponding to TU games, thereby providing two new versions of the …
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A complete reified temporal logic and its applications
… semantics or do not have a sound and complete axiomatization. In this thesis, a new complete reified temporal logic (CRTL) is introduced which has a clear syntax, semantics, and a complete axiomatic system by inheriting from the initial first order language. This is the main improvement made to …