230:
when applied to A asserts that "('diamond')A" is true in world i if and only if A is true in some worlds (at least one) accessible to world i. The exact semantic content of these assertions therefore depends crucially on the nature of the accessibility relation. For example, is world i accessible from itself? The answer to this question characterizes the precise nature of the system, and many exist, answering moral and temporal questions (in a temporal system, the accessibility relation relates states or 'instants' and only the future is accessible from a given moment. The
Necessity operator corresponds to 'for all future moments' in this logic. The operators are related to one another by similar
104:): a functor can be regarded as an "incomplete" expression with argument places to fill in. If we fill them in with appropriate subexpressions, then the resulting entirely completed expression can be regarded as a result, an output. Thus, a functor acts like a function sign, taking on input expressions, resulting in a new, output expression.
184:
often preceded the finding of their corresponding formal semantics. Intensional logic is not alone in that: also
Gottlob Frege accompanied his (extensional) calculus with detailed explanations of the semantical motivations, but the formal foundation of its semantics appeared only in the 20th century.
229:
of semantics) as quantifying over possible worlds. For example, the
Necessity operator (the 'box') when applied to a sentence A says 'The sentence "('box')A" is true in world i if and only if it is true in all worlds accessible from world i'. The corresponding Possibility operator (the 'diamond')
72:
as manifested in language (abstracting from any underlying psychological or biological processes). Logic is not a closed, completed science, and presumably, it will never stop developing: the logical analysis can penetrate into varying depths of the language (sentences regarded as atomic, or
326:. The semantical motivations were explained expressively, of course without those tools that we now use for establishing semantics for modal logic in a formal way, because they had not been invented then: Church did not provide formal semantic definitions.
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its input(s) into the extension of its output. Of course, it is assumed that we can do so at all: the extension of input expression(s) determines the extension of the resulting expression. Functors for which this assumption does not hold are called
238:). I.e., Something is necessary if and only if its negation is not possible, i.e. inconsistent. Syntactically, the operators are not quantifiers, they do not bind variables, but govern whole sentences. This gives rise to the problem of
224:
Modal logic can be regarded also as the most simple appearance of such studies: it extends extensional logic just with a few sentential functors: these are intensional, and they are interpreted (in the
92:
In order to achieve its special goal, logic was forced to develop its own formal tools, most notably its own grammar, detached from simply making direct use of the underlying natural language.
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is historically the earliest area in the study of intensional logic, originally motivated by formalizing "necessity" and "possibility" (recently, this original motivation belongs to
110:
links expressions of language to the outside world. Also logical semantics has developed its own structure. Semantic values can be attributed to expressions in basic categories: the
149:
cannot reach inside such fine logical structures of the language, but stops at a coarser level. The attempts for such deep logical analysis have a long past: authors as early as
180:
As mentioned, motivations for settling problems that belong today to intensional logic have a long past. As for attempts of formalizations, the development of
703:. Original: “The Development of Logic”. Translation of the title of the Appendix by Ruzsa, present only in Hungarian publication: “The last two decades”.
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Thus sometimes similar patterns repeated themselves for the history of development of intensional logic like earlier for that of extensional logic.
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functor we can in a sense abstract from the "material" part of its inputs and output, and regard the functor as a function turning directly the
242:, i.e. the problem of quantifying over or 'into' modal contexts. The operators appear in the grammar as sentential functors, they are called
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was built in a purely semantical way: a simpler treatment became possible, thank to the new formal tools invented since Church's work.
177:. These semantic values can be interpreted, transferred also for functors (except for intensional functors, they have only intension).
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As for functors, some of them are simpler than others: extension can be attributed to them in a simple way. In case of a so-called
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splitting them to predicates applied to individual terms, or even revealing such fine logical structures like
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to those relating existential and universal quantifiers (for example by the analogous correspondents of
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approach enabled more exact study of semantical questions. Exact formalization resulted in
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There are some intensional logic systems that claim to fully analyze the common language:
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of an individual name (the "designated" object named by that) is called its
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680:. Translation of the title: “Classical, modal and intensional logic”.
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173:: sentences (and individual terms) have both an extension and an
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722:. Translation of the title: “Syntax and semantics of logic”.
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Ruzsa, Imre (1987), "Függelék. Az utolsó két évtized", in
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Translation of the title: “Introduction to modern logic”.
711:(in Hungarian), vol. 1, Budapest: Akadémiai Kiadó,
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290:. His work was motivated by establishing the notion of
749:, Osiris tankönyvek (in Hungarian), Budapest: Osiris,
692:(in Hungarian), Budapest: Gondolat, pp. 695–734,
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introduced a distinction between two semantic values
221:, just one of the many branches of modal logic).
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47:that may have such individuals as their value (
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267:modality the modal functor is applied to an
669:(in Hungarian), Budapest: Akadémiai Kiadó,
667:Klasszikus, modális és intenzionális logika
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730:, vol. 2, Budapest: Akadémiai Kiadó,
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263:modalities: said in recent terms, in the
631:(2004). First-order intensional logic.
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782:Stanford Encyclopedia of Philosophy
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688:, William; Kneale, Martha (eds.),
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314:Type-theoretical intensional logic
286:Modern modal logic began with the
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709:Logikai szintaxis Ă©s szemantika
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648:is used in this article.
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19:Not to be confused with
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983:Propositional attitudes
651:Melvin Fitting (2007).
1472:Philosophy of language
1109:Inalienable possession
1089:Free choice inferences
1084:Faultless disagreement
855:Generalized quantifier
167:intensional statements
143:intensional statements
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1261:Inquisitive semantics
1226:Alternative semantics
356:Frege–Church ontology
288:Clarence Irving Lewis
1352:Function application
1159:Responsive predicate
1149:Privative adjectives
745:Ruzsa, Imre (2000),
726:Ruzsa, Imre (1989),
707:Ruzsa, Imre (1988),
665:Ruzsa, Imre (1984),
161:developed a kind of
122:is their extension.
1508:Philosophical logic
1503:Non-classical logic
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1402:Strawson entailment
1347:Existential closure
1291:Situation semantics
1194:Temperature paradox
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1129:Modal subordination
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1064:Discourse relations
773:"Intensional logic"
366:Temperature paradox
240:referential opacity
55:sense and reference
1482:Semantics of logic
1407:Strict conditional
1377:Quantifier raising
1342:Downward entailing
1322:Autonomy of syntax
1251:Generative grammar
1231:Categorial grammar
1169:Scalar implicature
1074:Epistemic modality
1049:De dicto and de re
690:A logika fejlődése
644:2008-07-04 at the
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771:Fitting, Melvin.
653:Intensional Logic
318:Already in 1951,
147:Extensional logic
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1044:Cumulativity
963:Indexicality
943:Definiteness
938:Conditionals
865:Logical form
780:
746:
727:
708:
689:
666:
656:
632:
609:
582:
525:
513:
486:
474:
462:
457:, p. 24
442:, p. 22
427:, p. 21
420:
415:, p. 12
408:
403:, p. 13
396:
391:, p. 10
384:
328:
317:
285:
264:
259:
255:
248:
223:
213:
187:
179:
146:
140:
135:
131:extension of
130:
126:
124:
106:
101:
97:
91:
64:
48:
38:
26:
25:
1327:Context set
1301:Type theory
1184:Subtrigging
948:Disjunction
875:Proposition
329:Later, the
304:Saul Kripke
215:Modal logic
210:Modal logic
204:Modal logic
198:Modal logic
136:intensional
127:extensional
120:truth value
1497:Categories
1477:Pragmatics
1124:Mirativity
890:Speech act
845:Entailment
840:Denotation
655:. In the
623:References
614:Ruzsa 1989
602:Ruzsa 2000
587:Ruzsa 2000
575:Ruzsa 2000
560:Ruzsa 2000
545:Ruzsa 2000
530:Ruzsa 2000
518:Ruzsa 2000
506:Ruzsa 2000
491:Ruzsa 1987
479:Ruzsa 2000
467:Ruzsa 2000
455:Ruzsa 2000
440:Ruzsa 2000
425:Ruzsa 2000
413:Ruzsa 2000
401:Ruzsa 2000
389:Ruzsa 2000
277:quantifier
155:syllogisms
50:intensions
40:extensions
1276:Mereology
1212:Formalism
1094:Givenness
1019:Cataphora
1007:Phenomena
998:Vagueness
928:Ambiguity
880:Reference
860:Intension
850:Extension
371:Relevance
251:Aristotle
232:dualities
227:metarules
175:intension
151:Aristotle
116:extension
112:reference
108:Semantics
87:epistemic
70:deduction
1430:See also
1315:Concepts
1189:Telicity
1024:Coercion
978:Negation
973:Modality
923:Anaphora
642:Archived
345:See also
324:calculus
260:de dicto
169:, Frege
98:sentence
94:Functors
79:temporal
61:Overview
933:Binding
779:(ed.).
258:versus
182:calculi
89:ones).
83:dynamic
1362:Monads
909:Topics
753:
734:
715:
696:
686:Kneale
673:
294:. The
279:whose
1054:De se
958:Focus
916:Areas
885:Scope
775:. In
377:Notes
281:scope
275:by a
273:bound
265:de re
256:de re
75:modal
66:Logic
45:terms
751:ISBN
732:ISBN
713:ISBN
694:ISBN
671:ISBN
100:and
1306:TTR
1499::
594:^
567:^
552:^
537:^
498:^
447:^
432:^
306:,
246:.
157:.
145:.
138:.
85:,
81:,
77:,
57:.
813:e
806:t
799:v
785:.
741:.
661:.
23:.
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