02628nam a2200385 i 4500991003319429707536170126t20142014sz a b 001 0 eng d9783319017204 (pbk.)3319017209 (pbk.)b14315191-39ule_instBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematicaeng511.4223AMS 49J45AMS 74Q10AMS 49J40AMS 74Q05LC QA3.L28Modal interval analysis :new tools for numerical information /Miguel A. Sainz ... [et al.]Cham :Springer,c2014xvi, 316 p. :ill. ;24 cmtexttxtrdacontentunmediatednrdamediavolumencrdacarrierLecture notes in mathematics,0075-8434 ;2091Includes bibliographical references (pages 307-311) and index1. Intervals ; 2. Modal intervals ; 3. Modal interval extensions ; 4. Interpretability and optimality ; 5. Interval arithmetic ; 6. Equations and systems ; 7. Twins and f * algorithm ; 8. Marks ; 9. Intervals of marks ; 10. Some related problemsThis book presents an innovative new approach to interval analysis. Modal Interval Analysis (MIA) is an attempt to go beyond the limitations of classic intervals in terms of their structural, algebraic and logical features. The starting point of MIA is quite simple: It consists in defining a modal interval that attaches a quantifier to a classical interval and in introducing the basic relation of inclusion between modal intervals by means of the inclusion of the sets of predicates they accept. This modal approach introduces interval extensions of the real continuous functions, identifies equivalences between logical formulas and interval inclusions, and provides the semantic theorems that justify these equivalences, along with guidelines for arriving at these inclusions. Applications of these equivalences in different areas illustrate the obtained results. The book also presents a new interval object: marks, which aspire to be a new form of numerical treatment of errors in measurements and computationsInterval analysis (Mathematics)Sainz, Miguel A..b1431519107-02-1726-01-17991003319429707536LE013 65G SAI11 (2014)12013000293950le013pE44.99-l- 01010.i1579586x07-02-17Modal interval analysis1395512UNISALENTOle01326-01-17ma -engsz 00