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### Alternative axiomatizations of elementary probability theory

William K. Goosens
1979 Notre Dame Journal of Formal Logic
Third, while both probabilities are simultaneously axiomatized, the resultant axioms are about as simple as the usual axiomatizations of conditional probability alone.  ...  Outline In this paper I offer some new axiomatizations of elementary (finite) probability theory. The new axiomatizations have the following distinctive features.  ...  Finally, how does KK compare in power to the axiomatizations of conditional probability that accept theses Tl through T5 exactly for consistent conditionalizations?  ...

### Deductive Systems in Traditional and Modern Logic

Alex Citkin, Urszula Wybraniec-Skardowska
2020 Axioms
Since its inception, logic has studied the acceptable rules of reasoning, the rules that allow us to pass from certain statements, serving as premises or assumptions, to a statement taken as a conclusion  ...  The volume is opened with paper [1] by P. Kulicki in which he looks back to the roots of Western logic and compares what we have achieved today with the legacy of Aristotle.  ...  Nasieniewski analyze the so called discussive logic introduced by Stanisław Jaśkowski, and this is probably the first fully formally formulated system of paraconsistent logic.  ...

### Page 9534 of Mathematical Reviews Vol. , Issue 2004m [page]

2004 Mathematical Reviews
For our complete axiomatization (Hilbert-style) we use one of the possible definitions of belief, namely as probability of (modal) necessity.  ...  ; Barcelona) Axiomatic extensions of the nilpotent minimum logic.  ...

### Page 2314 of Mathematical Reviews Vol. , Issue 2003d [page]

2003 Mathematical Reviews
Consequently its probability of truth will depend not only on the probabilities of the various propositions it might express, but also on the probabilities of the contexts determining which proposition  ...  are classical probabilities of truth.  ...

### P. S. Novikov, Elements of Mathematical Logic (Oliver and Boyd, Edinburgh, 1964), 308 pp., 50s

R. H. Stoothoff
1965 Proceedings of the Edinburgh Mathematical Society
In the penultimate chapter two systems of number-theory are developed: Axiomatic Arithmetic (comparable to standard systems of arithmetic including unrestricted mathematical induction), and Restricted  ...  in RA (i.e. from the other axioms of Axiomatic Arithmetic).  ...  The last two chapters, on axiomatic set theory and effective computability take up a hundred pages of the book.  ...

### Page 3753 of Mathematical Reviews Vol. , Issue 80J [page]

1980 Mathematical Reviews
Variant axiomatizations of differing strength are investigated. The relations of these various systems to one another snd to full numerical probability of the usual form are described.  ...  , the author shows that whereas the stronger of two comparable true theories is the closer to the truth, which is as it should be, it is also the case that the stronger of two comparable false theories  ...

### Dealing with logical omniscience

Joseph Y. Halpern, Riccardo Pucella
2007 Proceedings of the 11th conference on Theoretical aspects of rationality and knowledge - TARK '07
In particular, adding probabilities to the language allows for finer distinctions between different approaches.  ...  We examine four approaches for dealing with the logical omniscience problem and their potential applicability: the syntactic approach, awareness, algorithmic knowledge, and impossible possible worlds.  ...  The probability of a formula ϕ is then the probability of the set of worlds where ϕ is true. Clearly, if ϕ and ψ are logically equivalent, then (ϕ) = (ψ) will be true.  ...

### Comparative Evaluation of Fuzzy Axiomatic Design and IAMS Comprehensive VIKOR Approaches for Material Selection in Mechanical Design

Filippo Ceccanti, Alessandro Giorgetti, Carlo Cavallini, Gabriele Arcidiacono, Paolo Citti
2020 International journal of engineering research and technology
This paper makes a comparative evaluation of two important approaches to identify the best materials alternatives: the C-VIKOR and the Fuzzy Axiomatic Design.  ...  An evaluation of the results obtained is made to show the peculiarity of each of the two approaches.  ...  In particular, the original C-VIKOR results [17] will be compared with the results obtained by the use of Intuitionistic Fuzzy Axiomatic Design (FAD and WFAD).  ...

### Logic and intelligent interaction

Thomas Ågotnes, Johan van Benthem, Eric Pacuit
2009 Synthese
The resulting merge of ideas from dynamic logics and probability theory can handle more significant scenarios from the literature than the toy systems available so far.  ...  The resulting logic is sound and complete. It can be compared to variable-forgetting as abstraction from information, wherein agents become unaware of certain variables.  ...

### A logic with big-stepped probabilities that can model nonmonotonic reasoning of system P

Dragan Doder
2011 Publications de l'Institut Mathématique (Beograd)
We discuss the connection between previously developed logics and the two sublogics of the logic presented here.  ...  We develop a sound and strongly complete axiomatic system for probabilistic logic in which we can model nonmonotonic (or default) reasoning.  ...  Acknowledgments The author would like to thank the anonymous referee for the comments that have helped clarify a number of points, eliminate mistakes and improve the text.  ...

### Page 4023 of Mathematical Reviews Vol. 58, Issue 6 [page]

1979 Mathematical Reviews
The author compares propensity interpretations of probabilities (as objective dispositional properties associated with experimental arrangements) with frequency interpretations, making use of possi- ble  ...  partial linguistic grammar can and should be for- mulated as an applied axiomatic theory in the language of predi- cate logic or set theory.  ...

### Page 6905 of Mathematical Reviews Vol. , Issue 2001J [page]

2001 Mathematical Reviews
The paper is a comparative study of two propositional fuzzy log- ics based on Frank triangular norms, namely the S-fuzzy logics (t-norm based propositional fuzzy logics having the basic con- nectives conjunction  ...  We may define a one-place probability operator, absolute probability, and then define conditional probability as a quotient of absolute probabilities, provided the denominator of the quotient is not zero  ...

### Page 846 of Mathematical Reviews Vol. 43, Issue 4 [page]

1972 Mathematical Reviews
Axiomatic deductive systems are compared to the | natural systems and also studied for themselves.  ...  Moreover, as in the more recent developments, various first-order languages are distinguished by their sets of non- logical constants so that each axiomatic science can be thought of as having its own  ...

### Page 2725 of Mathematical Reviews Vol. , Issue 2004d [page]

2004 Mathematical Reviews
“Representation and uniqueness theorems for the axiomatization demonstrate that the resulting generalization is comparable in mathematical richness to finitely additive probability theory.” 2004d:03031  ...  It is shown that the axiomatization is a generalization of conditional probability in which a principle of conditional probability that has been repeatedly criticized on normative grounds may fail.  ...

### A new axiomatization of unified quantum logic

M. Pavičić
1992 International Journal of Theoretical Physics
A statistical basis for this propositional logical system is given so as to interpret unified quantum logic as a system of deduction. The soundness and completeness of algebraic semantics are proved.  ...  Unified quantum logic which is a propositional logic underlying quantum formalism is given a new much simplified axiomatization.  ...  In this section we present a much simplified axiomatization of unified quantum logic. (See Theorem 1 given below when comparing the axiomatization with the one presented in Ref. [30] .)  ...
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