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Axioms for real-time logics [chapter]

J. -F. Raskin, P. -Y. Schobbens, T. A. Henzinger
1998 Lecture Notes in Computer Science  
This paper presents a complete axiomatization of two decidable propositional real-time linear temporal logics: Event Clock Logic (EventClockTL) and Metric Interval Temporal Logic with past (MetricIntervalTL  ...  Our proof is structured to yield axiomatizations also for interesting fragments of these logics, such as the linear temporal logic of the real numbers (TLR).  ...  In [17] , axioms for real-time logics are proposed.  ... 
doi:10.1007/bfb0055625 fatcat:jstank2yizdixgrdxkjgzsthdm

Axioms for real-time logics

P.-Y. Schobbens, J.-F. Raskin, T.A. Henzinger
2002 Theoretical Computer Science  
This paper presents a complete axiomatization of two decidable propositional real-time linear temporal logics: Event Clock Logic (EventClockTL) and Metric Interval Temporal Logic with past (MetricIntervalTL  ...  Our proof is structured to yield axiomatizations also for interesting fragments of these logics, such as the linear temporal logic of the real numbers (TLR).  ...  In [17] , axioms for real-time logics are proposed.  ... 
doi:10.1016/s0304-3975(00)00308-x fatcat:j2t437tyg5ftrkgv3z3amqq4lq

Putting time into proof outlines [chapter]

Fred B. Schneider, Bard Bloom, Keith Marzullo
1992 Lecture Notes in Computer Science  
A logic for reasoning about timing properties of concurrent programs is presented.  ...  The correctness proof for a mutual exclusion protocol that uses execution timings in a subtle way illustrates the logic in action.  ...  Acknowledgements We are grateful to Limor Fix for extensive comments, and Georges Lauri for preliminary work on the soundness proof.  ... 
doi:10.1007/bfb0032010 fatcat:fcp4whn3ljhvdicaklpbuzpiu4

Axiomatizations for Temporal Epistemic Logic with Perfect Recall over Linear Time

Szabolcs Mikulas, Mark Reynolds, Tim French
2009 2009 16th International Symposium on Temporal Representation and Reasoning  
In particular, we present temporal epistemic logics for each of the following flows of time: arbitrary linear orders; the integers; the rationals; the reals; and for uniform flows of time.  ...  This paper presents various semantic interpretations for logics of knowledge and time with prefect recall.  ...  THE REALS We now present an axiomatization for logics of knowledge with perfect recall over real flows of time.  ... 
doi:10.1109/time.2009.18 dblp:conf/time/MikulasRF09 fatcat:z6njc4epjjhrtpeuhsakebuauq

Page 448 of American Mathematical Society. Bulletin of the American Mathematical Society Vol. 8, Issue [page]

1902 American Mathematical Society. Bulletin of the American Mathematical Society  
In the case before us, where we are concerned with the axioms of real numbers in arithmetic, the proof of the compatibility of the axioms is at the same time the proof of the mathematical existence of  ...  So, for example, a real number whose square is —1 does not exist mathe- matically.  ... 

Vienna Circle and Logical Analysis of Relativity Theory [chapter]

H. Andréka, J. X. Madarász, I. Németi, P. Németi, G. Székely
2011 Der Wiener Kreis in Ungarn / The Vienna Circle in Hungary  
It should be absolutely understandable for any reader what the axioms say and the reader can decide about each axiom whether he likes it.  ...  We investigate which axioms are needed for which predictions of RT. We want to make RT more transparent logically, easier to understand, easier to change, modular, and easier to teach.  ...  IND is a first-order logic approximation of the second-order logic continuity axiom of the real numbers, and it belongs to the methodology developed in FOM and in reverse mathematics that AxField strengthened  ... 
doi:10.1007/978-3-7091-0177-3_11 fatcat:xqlccf3xhbhnzl63ir6qhufugm

Was the Axiom of Reducibility a Principle of Logic?

Bernard Linsky
1990 Russell: the Journal of Bertrand Russell Studies  
What reasons does Russell actually give for doubting its logical status? Are they good reasons? I.  ...  I want to consider this criticism of the axiom from several points of view. Why is it thought that the axiom of reducibility is not a principle of logic?  ...  In fact, I believe, the ontology he had in the background in PM is what provided the justification for the axiom at that time.  ... 
doi:10.15173/russell.v10i2.1775 fatcat:aik6nufrbzgfjezfn5ayoafnxa

Completeness of neighbourhood logic

R Barua
2000 Journal of Logic and Computation  
This paper presents a completeness result for a first-order interval temporal logic, called Neighbourhood Logic (NL) which has two neighbourhood modalities.  ...  NL can support the specification of liveness and fairness properties of computing systems as well as formalisation of many concepts of real analysis.  ...  Time requirements -both qualitative as well as quantitative -have to be considered to reason about such systems. Thus, for such purposes one has to consider a real-time logic.  ... 
doi:10.1093/logcom/10.2.271 fatcat:yxhgky52gbdwroztq6nmiytfoa

Formal Verification of Control Systems Properties with Theorem Proving

Dejanira Araiza-Illan, Kerstin Eder, Arthur Richards
2014 arXiv   pre-print
For the systems, modelled in Simulink, we propose three main steps to achieve the verification: specifying the properties of interest over the signals within the model using Simulink blocks, an automatic  ...  We present a methodology to specify the properties in the model and a library of relevant assertion blocks (logic expressions), currently in development.  ...  They receive an integer (time sample) and produce a real (the signal value at that time).  ... 
arXiv:1405.7615v1 fatcat:u2gnlib7r5ev5gywitxpegxl3y

Completeness of Neighbourhood Logic [chapter]

Rana Barua, Suman Roy, Zhou Chaochen
1999 Lecture Notes in Computer Science  
This paper presents a completeness result for a first-order interval temporal logic, called Neighbourhood Logic (NL) which has two neighbourhood modalities.  ...  NL can support the specification of liveness and fairness properties of computing systems as well as formalisation of many concepts of real analysis.  ...  Time requirements -both qualitative as well as quantitative -have to be considered to reason about such systems. Thus, for such purposes one has to consider a real-time logic.  ... 
doi:10.1007/3-540-49116-3_49 fatcat:tu5erllpkzdaxaz33yehxfypzm

Verification of a Leader Election Algorithm in Timed Asynchronous Systems [chapter]

Neeraj Jaggi, K. Gopinath
2001 Lecture Notes in Computer Science  
The Timed Asynchronous System (TAS) model [3] has less stringent assumptions than the synchronous model but is still strong enough to serve as a foundation for the construction of dependable applications  ...  The PVS theorem prover is used for modelling and verification of the algorithms.  ...  Acknowledgements Thanks to the anonymous referees for their valuable comments and John Rushby and N.  ... 
doi:10.1007/3-540-45294-x_18 fatcat:xzxx2q2eunf7tlcmjgtj75qg34

On Logical Analysis of Relativity Theories [article]

Hajnal Andréka and István Németi and Judit X. Madarász and Gergely Székely
2011 arXiv   pre-print
The aim of this paper is to give an introduction to our axiomatic logical analysis of relativity theories.  ...  This research is supported by the Hungarian Scientific Research Fund for basic research grant No. T81188, as well as by a Bolyai grant for J. X. Madarász. ON LOGICAL ANALYSIS OF RELATIVITY THEORIES  ...  Therefore, in our first axiom, we state some usual properties of addition + and multiplication · true for real numbers.  ... 
arXiv:1105.0885v1 fatcat:mwrqce6jivdovk2pvkjowgzfy4

The Resolution of the Great 20th Century Debate in the Foundations of Mathematics

Edgar E. Escultura
2016 Advances in Pure Mathematics  
The issue: which one provides firm foundations for mathematics? None of them won the debate.  ...  The paper resolves the great debate of the 20 th century between the three philosophies of mathematics-logicism, intuitionism and formalism-founded by , respectively.  ...  In the new real number system R * of which the real number system R is a subspace, the concept nonterminating decimal is defined for the first time [16] [17] but has contained ambiguity.  ... 
doi:10.4236/apm.2016.63012 fatcat:ryvdb4hddbgetdlf7jwgbb5iaa

An Adequate First Order Interval Logic [chapter]

Zhou Chaochen, Michael R. Hansen
1998 Lecture Notes in Computer Science  
Introduction Interval temporal logics, based on ITL 11], have shown to be useful for the speci cation and veri cation of safety properties of real-time systems.  ...  A complete rst order logic for the neighbourhood modalities is presented.  ...  A Completeness result for NL So far, real numbers (R) was used as the domain of time and values. It is well-known that it is impossible to have a complete axiomatization for the real numbers.  ... 
doi:10.1007/3-540-49213-5_23 fatcat:g4se6wk3zrd7tffhqhz7xbnppa

The Ways of Hilbert's Axiomatics: Structural and Formal [chapter]

Wilfried Sieg
2020 The Prehistory of Mathematical Structuralism  
the first time in Hilbert's talk in Leipzig in the fall of 1922.  ...  method during the 1890s, culminating in the Paris address of 1900, and the early 1920s, when the finitist consistency program developed in a methodologically coherent way; that program was presented for  ...  real numbers] took the largest space for a long time.  ... 
doi:10.1093/oso/9780190641221.003.0006 fatcat:yx6fp5nmozh33f3lquj3tofc2a
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