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Chagrov A., Zakharyaschev M. — Modal logic
Chagrov A., Zakharyaschev M. — Modal logic



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Название: Modal logic

Авторы: Chagrov A., Zakharyaschev M.

Аннотация:

Modal logic is a branch of mathematical logic studying mathematical models of correct reasoning which involves various kinds of necessity-like and possibility-like operators. The first modal systems were created in the 1910s and later by Lewis (cf. Lewis and Langford, 1932) who used the operators "it is necessary" and "it is possible" for analyzing other logical connectives, in particular implication. Orlov 1928) and Godel 1933) constructed modal systems with the operator "it is provable" and exploited them to interpret Heyting's intuitionistic logic. More recently numerous modal systems have originated from different sources.


Язык: en

Рубрика: Математика/Алгебра/Математическая логика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 605

Добавлена в каталог: 11.05.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$bb_n$      44
$bc_n$      43
$bd_n$      42 81
$btw_n$      55
$bw_n$      43 80
$den_n$      80
$ga_{klmn}$      79
$md(\varphi)$      65
$nf_n$      223
$tab_n$      417
$tra$      78
$tra_n$      79
$\mathbf B_n$      112
$\mathbf K$      69
$\mathbf K_n$      100
$\mathbf T$      91 116
$\mathbf T_n$      112
$\mathbf{Alt}_n$      116
$\mathbf{BD}_n$      112
$\mathbf{BTW}_n$      112
$\mathbf{BW}_n$      112
$\mathbf{Cl}$      6 112
$\mathbf{D4G}_i$      116
$\mathbf{D4}$      94
$\mathbf{D5}$      94
$\mathbf{D}$      93 116
$\mathbf{GL.3}$      157
$\mathbf{GL}$      94 116
$\mathbf{Grz.3}$      157
$\mathbf{Grz}$      93 116
$\mathbf{Int}$      28
$\mathbf{K4.1}$      116
$\mathbf{K4.2}$      116
$\mathbf{K4.3}$      116
$\mathbf{K4Alt}_n$      116
$\mathbf{K4BD}_n$      116
$\mathbf{K4BW}_n$      116
$\mathbf{K4B}$      116
$\mathbf{K4H}$      116
$\mathbf{K4Z}$      116
$\mathbf{K4}$      92 116
$\mathbf{K4}_{n,m}$      116
$\mathbf{K5}$      116
$\mathbf{KB}$      116
$\mathbf{KC}$      112
$\mathbf{KP}$      112
$\mathbf{LC}$      112
$\mathbf{ML}$      53
$\mathbf{ND}_k$      112
$\mathbf{NL}_n$      112
$\mathbf{S2}$      99
$\mathbf{S3}$      99
$\mathbf{S4.1}$      116
$\mathbf{S4.2}$      116
$\mathbf{S4.3}$      94
$\mathbf{S4}$      92 116
$\mathbf{S5}$      93 116
$\mathbf{S6}$      99
$\mathbf{Sub}\varphi$      4
$\mathbf{Sub}\varphi$-equivalent tableaux      140
$\mathbf{S}$      95
$\mathbf{Var}\mathcal L$      3
$\mathbf{Var}\varphi$      4
$\mathcal D$-persistence      354
$\mathcal L$      3
$\mathcal L$-formula      3
$\mathcal{CSF}$      380
$\mathcal{ML}$      61
$\mathcal{ML}$-formula      61
$\mathcal{QCSF}$      391
$\mathcal{QSF}$      391
$\mathcal{SF}$      380
$\Sigma$-equivalent points      140 268
$\varkappa$-approximability      120
A*      116
Actual world      154 240
Actual world condition      319
Admissible rule      16
Algebra      193
Algebra of formulas      195
Algebra of open elements      247
Algebra, boolean      206
Algebra, closure      247
Algebra, degenerate      194
Algebra, diagonalizable      214
Algebra, for a logic      198 214
Algebra, free of rank $\varkappa$      222
Algebra, Grzegorczyk      214
Algebra, Heyting      198
Algebra, interior      247
Algebra, Magarian      214
Algebra, modal      214
Algebra, pseudo-boolean      198
Algebra, pseudo-boolean, complete      202
Algebra, quotient      224
Algebra, recursive      498
Algebra, subdirectly irreducible      231
Algebra, Tarski — Lindenbaum      197
Algebra, topological boolean      214 247
Algebra, transitive      214
Algebra, well-connected      455
Alternative world      63
Alternativeness relation      63
Amalgamability      451
Antichain      43
Antichain, n-stable      406
Antichain, stable      406
Antisymmetry      25
Antitabularity      431 441
Arithmetic interpretation      94
atom      212
Atom in a frame      249
AWC      319
Axiom      9
Axiom scheme      12
Axiom, additional      110 113
Axiom, extra      110 113
Axiomatic basis      118
Axiomatization      115
Axiomatization, finite      110 113
Axiomatization, independent      16
Axiomatization, recursive      117
Axiomatization, recursively enumerable      117
Balloon      103
Balloon, reflexive      104
Bidual      243 245
Bisimulation      54
Boolean function      19
Branching      44
Branching, inner      423
Branching, outer      423
Bulldozing      72
Calculus      115
Canonical formula      310
Canonical formula, intuitionistic      310
Canonical formula, intuitionistic, negation free      310
Canonical formula, normal modal      310
Canonical formula, normal modal, negation free      310
Canonical formula, quasi-normal      320
Canonical formula, quasi-normal, negation free      320
CDC      298
Chain      32
Chain logic      119
Chain, ascending      32
Chain, descending      32
Characteristic formula      329
Church — Minsky thesis      493
Church's thesis      491
Cl      9
Class of frames, closed under subframes      383
Class of frames, intuitionistically definable      121
Class of frames, modally definable      121
Classical calculus      9
Classical logic      6
Classical model      5
Closed domain      302
Closed domain condition      298
Closure operation      247
Cluster      68
Cluster, degenerate      68
Cluster, final      70
Cluster, last      70
Cluster, proper      68
Cluster, simple      68
Codepth      166
Cofinal set      295
Cofinal subframe formula      313
Cofinal subframe logic      380
Cofinal subframe logic, quasi-normal      391
Completeness      14 45 91
Completeness, functional      58
Completeness, structural      16
Completeness, truth-functional      20 58
Complexity function      547
con      80
Conclusion      4
Configuration      493
Configuration problem      493
Congruence      224 262
Congruence rule      17 89
Conjunct      4
Conjunction      1 3
Connectedness      80
Connectedness, strong      40
Conservative formula      449 468
Consistency      16
Countermodel      5 26
Cover      70
Cut      409
Cyclic set      269
Cyclic set, d-      269
Cyclic set, degenerate      269
Cyclic set, non-degenerate      269
D      93
DA      36
Dead end      65
Decidability      6
Decidability of a property      536
Decidable set      492
Deductively equal formulas      115
Degree of Kripke incompleteness      364
density      79
Density, n-      79
Deontic necessity      62
Depth of a frame      43 81
Depth of a point      267
Derivable rule      16 88
Derivation      11 84 110
Derivation from assumptions      12 84 110
Derivation, length of      11
Derivation, substitutionless      12
Deterministic machine      557
Diagram of a frame      27 66
Diameter      563
dir      80
Direct product      220 249
Directedness      80
Directedness, downward      350
Directedness, strong      42
Disjoint union      34 265 267
Disjunct      4
Disjunction      1 3
Disjunction property      19 471
Disjunction property, modal      90 471
Disjunction property, weak      543
Disjunction, repeatless      111
Disjunction, weak      59
Distinguished element      194
Distinguished point      240
Distinguished world      99
Downward closed set      26
Dual of a frame      205 214 236 240
Dual of a matrix      216 245
Dual of an algebra      211 216 243 244
Dum      116
Dum.3      157
Dummett formula      36
Dummett logic      119
Elementarity, $\mathcal C$-      340
Elementary logic      166
Elementary, class of frames      166
Embedding      46 194
Embedding, quasi-      389
Epistemic necessity      62
EQUIVALENCE      4
Equivalence relation      93
Equivalence, polynomial      548
Equivalent, calculi      115
Equivalent, formulas      19
Equivalent, modalities      90
euc      80
Euclidean      80
Exponential approximability      119
Exponential approximability, hereditary      553
Expressibility      58
Expression      58
Extension of a logic      15 112
Extension of a logic, normal      113
Extension of a matrix      227
ExtInt      112
ExtL      112 113
Falsehood      3
Filter      207
Filter, critical      230
Filter, generated      208
Filter, maximal      211
Filter, normal      223
Filter, prime      210
Filter, principal      208
Filter, proper      207
Filtration      140
Filtration, coarsest      141
Filtration, finest      141
Filtration, Lemmon      142
Filtration, selective      149
Final state      493
Finite approximability      49 119
Finite approximability, global      121
Finite approximability, strict      361
Finite base over a model      142
Finite cofinal quasi-embedding property      389
Finite cover property      354
Finite depth logic      272
Finite embedding property      385
Finite frame property      49 119
Finite model property      119
First order frame      282
Focus      406
for      112 116
For$\mathcal L$      4
For$\mathcal{ML}$      61
Formula      1 3
Formula, $\Box\Diamond$-      379
Formula, antimonotone      20
Formula, atomic      3
Formula, classically established      59
Formula, conservative      449 468
Formula, derivable      11
Formula, derivable from assumptions      12
Formula, disjunction free      293
1 2 3
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