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Alternative axiomatizations of elementary probability theory

1979
*
Notre Dame Journal of Formal Logic
*

Third, while both

doi:10.1305/ndjfl/1093882420
fatcat:ongz33zrx5fdhjoz7bsznvu4ki
*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? ...##
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Deductive Systems in Traditional and Modern Logic

2020
*
Axioms
*

Since its inception,

doi:10.3390/axioms9030108
fatcat:hviq34mlgracri3qdsawrwfopi
*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

1965
*
Proceedings of the Edinburgh Mathematical Society
*

In

doi:10.1017/s0013091500008853
fatcat:bq7lupakqzcppo6fya6253nhwu
*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

2007
*
Proceedings of the 11th conference on Theoretical aspects of rationality and knowledge - TARK '07
*

In particular, adding

doi:10.1145/1324249.1324273
dblp:conf/tark/HalpernP07
fatcat:aa42ojvufjax7c4phtjky6xjja
*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

2020
*
International journal of engineering research and technology
*

This paper makes a

doi:10.37624/ijert/13.1.2020.80-87
fatcat:iqio5mshfvg73mfpczpepxpwhm
*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

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. ...

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

2011
*
Publications de l'Institut Mathématique (Beograd)
*

We discuss

doi:10.2298/pim1104013d
fatcat:3t2l4ey56zdlffixe2szjaeu7y
*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. ...##
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A new axiomatization of unified quantum logic

1992
*
International Journal of Theoretical Physics
*

A statistical basis for this propositional

doi:10.1007/bf00671784
fatcat:q62syndlhnetrdzqkfyw5atmrq
*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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