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Noncomparabilities & Nonstandard Logics

Robert C. Hockett
2006 Social Science Research Network  
A broader lesson is that nonstandard logics offer the best means of modeling relations among propositions postulated by any similarly -epistemically or "politically" -modest, "pragmatic" conception of  ...  The broader lesson here is that certain nonstandard logics offer a potentially useful means of modeling relations among propositions postulated by any epistemically or "politically" modest conception of  ... 
doi:10.2139/ssrn.931042 fatcat:65fxyphkizcp3pwtvc7sjutilm

Nonstandard Consequence Operators Generated By Mixed Logic-Systems [article]

Robert A. Herrmann
2010 arXiv   pre-print
Mixed logic-systems contain both standard and nonstandard coordinate values.  ...  In this paper, it is shown that each of the specifically defined mixed logic-systems generates an internal nonstandard consequence operator.  ...  A need has now arisen that requires the logic-system notion to be extended so that, after the language is properly embedded into the nonstandard structure -the Grundlegend or Extended Grundlegend Structure  ... 
arXiv:math/0412562v5 fatcat:v3ynztb4pnfpdpo2q6og2l5hdm

Nonstandard methods in many-valued logics

C. A. Drossos
1998 Soft Computing - A Fusion of Foundations, Methodologies and Applications  
In this paper we try to introduce some basic frameworks to study MV-algebras from a nonstandard point of view.  ...  Since MV-algebras include, in an essential way, infinitisimals it was felt that a systematic study of relationships of nonstandard methods and MV-algebras was needed.  ...  what Boolean algebras are to classical logic.  ... 
doi:10.1007/s005000050044 fatcat:hnert62ypnh2pdjnuhoek6xj7a

Extended Nonstandard Neutrosophic Logic, Set, and Probability based on Extended Nonstandard Analysis [article]

Florentin Smarandache
2019 arXiv   pre-print
Then, we extend the Nonstandard Neutrosophic Logic, Nonstandard Neutrosophic Set, and Nonstandard Probability on this Extended Nonstandard Analysis space - that we prove it is a nonstandard neutrosophic  ...  the unpierced binad - all these in order to close the newly extended nonstandard space under nonstandard addition, nonstandard subtraction, nonstandard multiplication, nonstandard division, and nonstandard  ...  Second Extension of Nonstandard Analysis For necessity of doing calculations that will be used in nonstandard neutrosophic logic in order to calculate the nonstandard neutrosophic logic operators (conjunction  ... 
arXiv:1903.04558v1 fatcat:w5oeqdw2qbbl3b2gcj6pjm7chu

Applications to a Realistic Physics [chapter]

1995 Nonstandard Logics and Nonstandard Metrics in Physics  
Nevertheless, these derives from large group of facts and circumstances similar to above examined, by simplest logic -if we agree to consider logic in contemporary physics at all!  ...  Schrödinger and de Broglie have pointed on the necessity to return to the mentioned concept and usual-logical methodology.  ... 
doi:10.1142/9789812796158_0004 fatcat:btafgrpibzan3dq2yg7wlg5tzq

Extended Nonstandard Neutrosophic Logic, Set, and Probability Based on Extended Nonstandard Analysis

Florentin Smarandache
2019 Zenodo  
the unpierced binad—all these in order to close the newly extended nonstandard space under nonstandard addition, nonstandard subtraction, nonstandard multiplication, nonstandard division, and nonstandard  ...  We extend for the second time the nonstandard analysis by adding the left monad closed to the right, and right monad closed to the left, while besides the pierced binad (we introduced in 1998) we add now  ...  Second Extension of Nonstandard Analysis For the necessity of doing calculations that will be used in nonstandard neutrosophic logic in order to calculate the nonstandard neutrosophic logic operators (  ... 
doi:10.5281/zenodo.2838678 fatcat:bcscpb67rzcjhb4fvtnu2a2flu

About Nonstandard Neutrosophic Logic (Answers to Imamura 'Note on the Definition of Neutrosophic Logic') [article]

Florentin Smarandache
2019 arXiv   pre-print
The paper intends to answer Imamura criticism that we found benefic in better understanding the nonstandard neutrosophic logic, although the nonstandard neutrosophic logic was never used in practical applications  ...  In order to more accurately situate and fit the neutrosophic logic into the framework of nonstandard analysis, we present the neutrosophic inequalities, neutrosophic equality, neutrosophic infimum and  ...  Takura Imamura for his interest and critics of Nonstandard Neutrosophic Logic, which eventually helped in improving it.  ... 
arXiv:1812.02534v2 fatcat:loabuaewjfdwrpbtihhdahzvmq

Extended Nonstandard Neutrosophic Logic, Set, and Probability Based on Extended Nonstandard Analysis

Smarandache
2019 Symmetry  
Then, we extend the Nonstandard Neutrosophic Logic, Nonstandard Neutrosophic Set, and Nonstandard Probability on this Extended Nonstandard Analysis space, and we prove that it is a nonstandard neutrosophic  ...  the unpierced binad—all these in order to close the newly extended nonstandard space under nonstandard addition, nonstandard subtraction, nonstandard multiplication, nonstandard division, and nonstandard  ...  extended nonstandard neutrosophic logic.  ... 
doi:10.3390/sym11040515 fatcat:eqofbwynsrdc3blk2kg3szr2ee

Nonstandard analysis in topology: nonstandard and standard compactifications

S. Salbany, Todor Todorov
2000 Journal of Symbolic Logic (JSL)  
Let (X, T) be a topological space and *X a nonstandard extension of X. Sets of the form *G. where G ∈ T, form a base for the "standard" topology S T on *X.  ...  Thus, * X, S T is a compact topo logical space. The sets * G, G ∈ T , constitute a base for S T .  ...  We shall show that these compactifications can also be obtained from nonstandard compactifications in a canonical way. The relevant reference for Frames (and also stable compactness) is P.  ... 
doi:10.2307/2695079 fatcat:dotl5j5cfnc7dc6awrscrvorzi

Completeness of Hoare Logic over Nonstandard Models [article]

Zhaowei Xu, Yuefei Sui, Wenhui Zhang
2017 arXiv   pre-print
The nonstandard approach to program semantics has successfully resolved the completeness problem of Floyd-Hoare logic.  ...  Then we define, based on the new semantics of while-programs, a new semantics of Hoare logic in nonstandard models of PA, and show that the standard axiom system of Hoare logic is sound and complete w.r.t  ...  Of special interest is the completeness of Hoare logic over nonstandard models.  ... 
arXiv:1703.00240v1 fatcat:oo6n3lds6jdsre3ygqj7uc4zve

Total correctness in nonstandard logics of programs

Ildikó Sain
1987 Theoretical Computer Science  
We show that termination is a first-order notion if approached via Nonstandard Logics of Programs (NLP).  ...  A comparison of the tea-proving powers of distinguished methods (or logics of programs) is also attempted.  ...  Total correctness in nonstandard logics of programs 305 3.1.  ... 
doi:10.1016/0304-3975(87)90118-6 fatcat:drq3xdpqebcethzcycdoklunya

Nonstandard conjunctions and implications in fuzzy logic

János C. Fodor, Tibor Keresztfalvi
1995 International Journal of Approximate Reasoning  
Three classes of nonstandard conjunctions and implications are formulated so that all of them satisfy the proposed axioms.  ...  We point out possible disadvantages of considering exclusively t-norms and t-conorms as proper models for conjunction and disjunction in fuzzy logic.  ...  INTRODUCTION The proper definition of connectives (conjunction, disjunction, negation, implication, etc.) is one of the most important problems in fuzzy logic.  ... 
doi:10.1016/0888-613x(94)00012-r fatcat:gnx645obordbni3zxodv6lpg3i

Hyperordinals and Nonstandard α-Models [chapter]

Mauro Nasso
2017 Logic and algebra  
Nonstandard α-Models We shall work in ZF − C, i.e. in Zermelo-Fraenkel axiomatic set theory ZF with choice but without the axiom Fnd of foundation (regularity).  ...  In this paper we extend the traditional set-theoretic notion of standard models and nonstandard models going up to α levels in the cumulative hierarchy, α any given limit ordinal.  ...  Call such an M a strong nonstandard α-model.  ... 
doi:10.1201/9780203748671-22 fatcat:hyzrqnkznrga7lepti433ft6he

The problem of formalization of some nonstandard semantics

Elena D. Smirnova
2004 Logic and Logical Philosophy  
THE PROBLEM OF FORMALIZATION OF SOME NONSTANDARD SEMANTICS * 1. I shall propose the formalization of some nonstandard semantics in sequential form.  ...  Now, let us consider the problem of the formalization of logics (resp. relations of logical entailment →), describe above. Let us formulate some well known logical systems in sequential form.  ... 
doi:10.12775/llp.2001.010 fatcat:42mu3njvfvcj3av6h5w6aglyge

About Nonstandard Neutrosophic Logic (Answers to Imamura's "Note on the Definition of Neutrosophic Logic")

Florentin Smarandache
2019 Zenodo  
In order to more accurately situate and fit the neutrosophic logic into the framework of nonstandard analysis, we present the neutrosophic inequalities, neutrosophic equality, neutrosophic infimum and  ...  supremum, neutrosophic standard intervals, including the cases when the neutrosophic logic standard and nonstandard components T, I, F get values outside of the classical unit interval [0, 1], and a brief  ...  Takura Imamura for his interest and critics of Nonstandard Neutrosophic Logic, which eventually helped in improving it.  ... 
doi:10.5281/zenodo.2837695 fatcat:xbqyekroo5gi3ny4l6wwaunkpa
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