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set predicate logic

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1 set predicate logic

теоретико-множественная логика предикатов

sequential logic element — элемент последовательности логики

resistor transistor logic — резисторно-транзисторная логика

programmable array logic — программируемая матричная логика

fault-masking logic — логика с маскированием неисправностей

character recognition logic — логика распознавания символов

The English-Russian dictionary general scientific > set predicate logic
2 set predicate logic

Математика: теоретико-множественная логика предикатов

Универсальный англо-русский словарь > set predicate logic
3 set-theoretic predicate logic

Математика: теоретико-множественная логика предикатов

Универсальный англо-русский словарь > set-theoretic predicate logic
4 set-theoretic predicate logic

теоретико-множественная логика предикатов

English-Russian scientific dictionary > set-theoretic predicate logic
5 logic

1) логика || логический

2) вчт логические схемы, логика

3) логический блок; логический узел

•

logic with identity — логика с тождеством

logic without identity — логика без тождества

- algebraic logic

- applied logic

- auxiliary logic

- bivalent logic

- cellular logic

- class logic

- classical logic

- classical propositional logic

- commodity logic

- continuous logic

- countably complete logic

- decision logic

- decoding logic

- deductive logic

- derivative logic

- deterministic logic

- dialectical logic

- digitizing logic

- dual logic

- dyadic logic

- dynamic logic

- elementary logic

- empirical logic

- equational logic

- extended logic

- extensional logic

- external logic

- feature logic

- finite-valued logic

- first-order logic

- free logic

- fuzzy logic

- general modal logic

- generalized logic

- generalized stochastic logic

- heuristic logic

- imperative logic

- implicational logic

- inductive logic

- inductively generated logic

- infinitary logic

- infinite-valued logic

- intensional logic

- intermediate logic

- intrinsic logic

- intuitionistic logic

- iterative logic

- lattice-theoretic logic

- limit logic

- logic of certainty

- logic of evidence

- logic of existence

- logic of higher order

- logic of modalities

- logic of norms

- logic of part

- logic of preference

- logic of strict implication

- logic of truth

- logic of verification

- logic of whole

- minimal logic

- modal logic

- monadic logic

- multivalued logic

- natural logic

- nonclassical logic

- nonconstructive logic

- nonmonotonic logic

- normative logic

- n-valued logic

- object logic

- orthodox logic

- polyvalent logic

- positive logic

- predicate logic

- projectively generated logic

- propositional logic

- pure logic

- quantificational logic

- quite full logic

- reduced logic

- redundant logic

- search logic

- semicomplete logic

- sentential logic

- separable logic

- set-theoretic predicate logic

- shielded

- situational logic

- static logic

- stochastic logic

- strict logic

- strongly strict logic

- superintuitionistic logic

- switching logic

- syllogistic logic

- system logic

- technical logic

- tense logic

- three-level logic

- three-valued logic

- topological logic

- traditional logic

- transforming logic

- trivalent logic

- unordered logic

- unorthodox logic

- unspecialized logic

English-Russian scientific dictionary > logic
6 predicate

1. n грам. лог. предикат, сказуемое

choice predicate — предикат выбора

predicate logic — логика предикатов

predicate language — язык предикатов

compound predicate — составное сказуемое

negated predicate — предикат с отрицанием

2. n лог. утверждение

3. a предикативный

predicate noun — предикативное существительное, существительное в роли именной части составного сказуемого

predicate node — предикативный узел

4. v утверждать; заявлять; делать заявление

my plan is predicated on the assumption that … — в своём плане я исхожу из того, что …

5. v грам. лог. предицировать

6. v наводить на мысль

grass predicates greenness — трава вызывает представление о зелёном цвете

7. v редк. проповедовать

8. v разг. предсказывать

Синонимический ряд:

1. assert (verb) affirm; assert; aver; avouch; avow; constate; declare; depose; maintain; mean; proclaim; profess; protest; set forth; state

2. establish (verb) base; bottom; build; establish; fasten; found; ground; rest; root in; seat; stay

English-Russian base dictionary > predicate
7 set-theoretic

теоретико-множественный set-theoretic predicate logic ≈ теоретико-множественная логика предикатов - set-theoretic geometry - set-theoretic interpretation - set-theoretic intersection - set-theoretic jog - set-theoretic operation - set-theoretic projection - set-theoretic statement - set-theoretic topology - set-theoretic union

Большой англо-русский и русско-английский словарь > set-theoretic
8 теоретико-множественная логика предикатов

Mathematics: set predicate logic, set-theoretic predicate logic

Универсальный русско-английский словарь > теоретико-множественная логика предикатов
9 теоретико-множественная логика предикатов

set-theoretic predicate logic

Русско-английский научно-технический словарь Масловского > теоретико-множественная логика предикатов
10 Artificial Intelligence

   1) Programs and the Complexity of Human Mental Processes

   In my opinion, none of [these programs] does even remote justice to the complexity of human mental processes. Unlike men, "artificially intelligent" programs tend to be single minded, undistractable, and unemotional. (Neisser, 1967, p. 9)

   2) Artificial Intelligence Is an Engineering Discipline

   Future progress in [artificial intelligence] will depend on the development of both practical and theoretical knowledge.... As regards theoretical knowledge, some have sought a unified theory of artificial intelligence. My view is that artificial intelligence is (or soon will be) an engineering discipline since its primary goal is to build things. (Nilsson, 1971, pp. vii-viii)

   3) A Sceptical View of Artificial Intelligence

   Most workers in AI [artificial intelligence] research and in related fields confess to a pronounced feeling of disappointment in what has been achieved in the last 25 years. Workers entered the field around 1950, and even around 1960, with high hopes that are very far from being realized in 1972. In no part of the field have the discoveries made so far produced the major impact that was then promised.... In the meantime, claims and predictions regarding the potential results of AI research had been publicized which went even farther than the expectations of the majority of workers in the field, whose embarrassments have been added to by the lamentable failure of such inﬂated predictions....

   When able and respected scientists write in letters to the present author that AI, the major goal of computing science, represents "another step in the general process of evolution"; that possibilities in the 1980s include an all-purpose intelligence on a human-scale knowledge base; that awe-inspiring possibilities suggest themselves based on machine intelligence exceeding human intelligence by the year 2000 [one has the right to be skeptical]. (Lighthill, 1972, p. 17)

   4) Just as Astronomy Succeeded Astrology, the Discovery of Intellectual Processes in Machines Should Lead to a Science, Eventually

   Just as astronomy succeeded astrology, following Kepler's discovery of planetary regularities, the discoveries of these many principles in empirical explorations on intellectual processes in machines should lead to a science, eventually. (Minsky & Papert, 1973, p. 11)

   5) Problems in Machine Intelligence Arise Because Things Obvious to Any Person Are Not Represented in the Program

   Many problems arise in experiments on machine intelligence because things obvious to any person are not represented in any program. One can pull with a string, but one cannot push with one.... Simple facts like these caused serious problems when Charniak attempted to extend Bobrow's "Student" program to more realistic applications, and they have not been faced up to until now. (Minsky & Papert, 1973, p. 77)

   6) The Meaning of a Symbolic Description

   What do we mean by [a symbolic] "description"? We do not mean to suggest that our descriptions must be made of strings of ordinary language words (although they might be). The simplest kind of description is a structure in which some features of a situation are represented by single ("primitive") symbols, and relations between those features are represented by other symbols-or by other features of the way the description is put together. (Minsky & Papert, 1973, p. 11)

   7) The Principle of Artificial Intelligence

   [AI is] the use of computer programs and programming techniques to cast light on the principles of intelligence in general and human thought in particular. (Boden, 1977, p. 5)

   8) Artificial Intelligence Recognizes the Need for Knowledge in Its Systems

   The word you look for and hardly ever see in the early AI literature is the word knowledge. They didn't believe you have to know anything, you could always rework it all.... In fact 1967 is the turning point in my mind when there was enough feeling that the old ideas of general principles had to go.... I came up with an argument for what I called the primacy of expertise, and at the time I called the other guys the generalists. (Moses, quoted in McCorduck, 1979, pp. 228-229)

   9) Artificial Intelligence Is Psychology in a Particularly Pure and Abstract Form

   The basic idea of cognitive science is that intelligent beings are semantic engines-in other words, automatic formal systems with interpretations under which they consistently make sense. We can now see why this includes psychology and artificial intelligence on a more or less equal footing: people and intelligent computers (if and when there are any) turn out to be merely different manifestations of the same underlying phenomenon. Moreover, with universal hardware, any semantic engine can in principle be formally imitated by a computer if only the right program can be found. And that will guarantee semantic imitation as well, since (given the appropriate formal behavior) the semantics is "taking care of itself" anyway. Thus we also see why, from this perspective, artificial intelligence can be regarded as psychology in a particularly pure and abstract form. The same fundamental structures are under investigation, but in AI, all the relevant parameters are under direct experimental control (in the programming), without any messy physiology or ethics to get in the way. (Haugeland, 1981b, p. 31)

    10) There Are Many Types of Reasoning

   There are many different kinds of reasoning one might imagine:

    Formal reasoning involves the syntactic manipulation of data structures to deduce new ones following prespecified rules of inference. Mathematical logic is the archetypical formal representation. Procedural reasoning uses simulation to answer questions and solve problems. When we use a program to answer What is the sum of 3 and 4? it uses, or "runs," a procedural model of arithmetic. Reasoning by analogy seems to be a very natural mode of thought for humans but, so far, difficult to accomplish in AI programs. The idea is that when you ask the question Can robins ﬂy? the system might reason that "robins are like sparrows, and I know that sparrows can ﬂy, so robins probably can ﬂy."

    Generalization and abstraction are also natural reasoning process for humans that are difficult to pin down well enough to implement in a program. If one knows that Robins have wings, that Sparrows have wings, and that Blue jays have wings, eventually one will believe that All birds have wings. This capability may be at the core of most human learning, but it has not yet become a useful technique in AI.... Meta- level reasoning is demonstrated by the way one answers the question What is Paul Newman's telephone number? You might reason that "if I knew Paul Newman's number, I would know that I knew it, because it is a notable fact." This involves using "knowledge about what you know," in particular, about the extent of your knowledge and about the importance of certain facts. Recent research in psychology and AI indicates that meta-level reasoning may play a central role in human cognitive processing. (Barr & Feigenbaum, 1981, pp. 146-147)

    11) Programs Are Beginning to Do Things That Critics Have Asserted to Be Impossible

   Suffice it to say that programs already exist that can do things-or, at the very least, appear to be beginning to do things-which ill-informed critics have asserted a priori to be impossible. Examples include: perceiving in a holistic as opposed to an atomistic way; using language creatively; translating sensibly from one language to another by way of a language-neutral semantic representation; planning acts in a broad and sketchy fashion, the details being decided only in execution; distinguishing between different species of emotional reaction according to the psychological context of the subject. (Boden, 1981, p. 33)

    12) The Synthesis of Man and Machine

   Can the synthesis of Man and Machine ever be stable, or will the purely organic component become such a hindrance that it has to be discarded? If this eventually happens-and I have... good reasons for thinking that it must-we have nothing to regret and certainly nothing to fear. (Clarke, 1984, p. 243)

    13) The Thesis of Good Old-Fashioned Artificial Intelligence (GOFAI)

   The thesis of GOFAI... is not that the processes underlying intelligence can be described symbolically... but that they are symbolic. (Haugeland, 1985, p. 113)

    14) Artificial Intelligence Provides a Useful Approach to Psychological and Psychiatric Theory Formation

   It is all very well formulating psychological and psychiatric theories verbally but, when using natural language (even technical jargon), it is difficult to recognise when a theory is complete; oversights are all too easily made, gaps too readily left. This is a point which is generally recognised to be true and it is for precisely this reason that the behavioural sciences attempt to follow the natural sciences in using "classical" mathematics as a more rigorous descriptive language. However, it is an unfortunate fact that, with a few notable exceptions, there has been a marked lack of success in this application. It is my belief that a different approach-a different mathematics-is needed, and that AI provides just this approach. (Hand, quoted in Hand, 1985, pp. 6-7)

    15) Four Kinds of Artificial Intelligence

   We might distinguish among four kinds of AI.

   ♦ Nonpsychological AI

   Research of this kind involves building and programming computers to perform tasks which, to paraphrase Marvin Minsky, would require intelligence if they were done by us. Researchers in nonpsychological AI make no claims whatsoever about the psychological realism of their programs or the devices they build, that is, about whether or not computers perform tasks as humans do.

   ♦ Weak Psychological AI

   Research here is guided by the view that the computer is a useful tool in the study of mind. In particular, we can write computer programs or build devices that simulate alleged psychological processes in humans and then test our predictions about how the alleged processes work. We can weave these programs and devices together with other programs and devices that simulate different alleged mental processes and thereby test the degree to which the AI system as a whole simulates human mentality. According to weak psychological AI, working with computer models is a way of refining and testing hypotheses about processes that are allegedly realized in human minds.

   ♦ Strong Psychological AI

... According to this view, our minds are computers and therefore can be duplicated by other computers. Sherry Turkle writes that the "real ambition is of mythic proportions, making a general purpose intelligence, a mind." (Turkle, 1984, p. 240) The authors of a major text announce that "the ultimate goal of AI research is to build a person or, more humbly, an animal." (Charniak & McDermott, 1985, p. 7)

   ♦ Suprapsychological AI

   Research in this field, like strong psychological AI, takes seriously the functionalist view that mentality can be realized in many different types of physical devices. Suprapsychological AI, however, accuses strong psychological AI of being chauvinisticof being only interested in human intelligence! Suprapsychological AI claims to be interested in all the conceivable ways intelligence can be realized. (Flanagan, 1991, pp. 241-242)

    16) Determination of Relevance of Rules in Particular Contexts

   Even if the [rules] were stored in a context-free form the computer still couldn't use them. To do that the computer requires rules enabling it to draw on just those [ rules] which are relevant in each particular context. Determination of relevance will have to be based on further facts and rules, but the question will again arise as to which facts and rules are relevant for making each particular determination. One could always invoke further facts and rules to answer this question, but of course these must be only the relevant ones. And so it goes. It seems that AI workers will never be able to get started here unless they can settle the problem of relevance beforehand by cataloguing types of context and listing just those facts which are relevant in each. (Dreyfus & Dreyfus, 1986, p. 80)

    17) Form and Content Are Not Fundamentally Different

   Perhaps the single most important idea to artificial intelligence is that there is no fundamental difference between form and content, that meaning can be captured in a set of symbols such as a semantic net. (G. Johnson, 1986, p. 250)

    18) The Assumption That the Mind Is a Formal System

   Artificial intelligence is based on the assumption that the mind can be described as some kind of formal system manipulating symbols that stand for things in the world. Thus it doesn't matter what the brain is made of, or what it uses for tokens in the great game of thinking. Using an equivalent set of tokens and rules, we can do thinking with a digital computer, just as we can play chess using cups, salt and pepper shakers, knives, forks, and spoons. Using the right software, one system (the mind) can be mapped into the other (the computer). (G. Johnson, 1986, p. 250)

    19) A Statement of the Primary and Secondary Purposes of Artificial Intelligence

   The primary goal of Artificial Intelligence is to make machines smarter.

   The secondary goals of Artificial Intelligence are to understand what intelligence is (the Nobel laureate purpose) and to make machines more useful (the entrepreneurial purpose). (Winston, 1987, p. 1)

    20) Mathematical Logic Provides the Basis for Theory in AI

   The theoretical ideas of older branches of engineering are captured in the language of mathematics. We contend that mathematical logic provides the basis for theory in AI. Although many computer scientists already count logic as fundamental to computer science in general, we put forward an even stronger form of the logic-is-important argument....

   AI deals mainly with the problem of representing and using declarative (as opposed to procedural) knowledge. Declarative knowledge is the kind that is expressed as sentences, and AI needs a language in which to state these sentences. Because the languages in which this knowledge usually is originally captured (natural languages such as English) are not suitable for computer representations, some other language with the appropriate properties must be used. It turns out, we think, that the appropriate properties include at least those that have been uppermost in the minds of logicians in their development of logical languages such as the predicate calculus. Thus, we think that any language for expressing knowledge in AI systems must be at least as expressive as the first-order predicate calculus. (Genesereth & Nilsson, 1987, p. viii)

    21) Perceptual Structures Can Be Represented as Lists of Elementary Propositions

   In artificial intelligence studies, perceptual structures are represented as assemblages of description lists, the elementary components of which are propositions asserting that certain relations hold among elements. (Chase & Simon, 1988, p. 490)

    22) Definitions of Artificial Intelligence

   Artificial intelligence (AI) is sometimes defined as the study of how to build and/or program computers to enable them to do the sorts of things that minds can do. Some of these things are commonly regarded as requiring intelligence: offering a medical diagnosis and/or prescription, giving legal or scientific advice, proving theorems in logic or mathematics. Others are not, because they can be done by all normal adults irrespective of educational background (and sometimes by non-human animals too), and typically involve no conscious control: seeing things in sunlight and shadows, finding a path through cluttered terrain, fitting pegs into holes, speaking one's own native tongue, and using one's common sense. Because it covers AI research dealing with both these classes of mental capacity, this definition is preferable to one describing AI as making computers do "things that would require intelligence if done by people." However, it presupposes that computers could do what minds can do, that they might really diagnose, advise, infer, and understand. One could avoid this problematic assumption (and also side-step questions about whether computers do things in the same way as we do) by defining AI instead as "the development of computers whose observable performance has features which in humans we would attribute to mental processes." This bland characterization would be acceptable to some AI workers, especially amongst those focusing on the production of technological tools for commercial purposes. But many others would favour a more controversial definition, seeing AI as the science of intelligence in general-or, more accurately, as the intellectual core of cognitive science. As such, its goal is to provide a systematic theory that can explain (and perhaps enable us to replicate) both the general categories of intentionality and the diverse psychological capacities grounded in them. (Boden, 1990b, pp. 1-2)

    23) The Computer Can Not Be a Model of the Mind

   Because the ability to store data somewhat corresponds to what we call memory in human beings, and because the ability to follow logical procedures somewhat corresponds to what we call reasoning in human beings, many members of the cult have concluded that what computers do somewhat corresponds to what we call thinking. It is no great difficulty to persuade the general public of that conclusion since computers process data very fast in small spaces well below the level of visibility; they do not look like other machines when they are at work. They seem to be running along as smoothly and silently as the brain does when it remembers and reasons and thinks. On the other hand, those who design and build computers know exactly how the machines are working down in the hidden depths of their semiconductors. Computers can be taken apart, scrutinized, and put back together. Their activities can be tracked, analyzed, measured, and thus clearly understood-which is far from possible with the brain. This gives rise to the tempting assumption on the part of the builders and designers that computers can tell us something about brains, indeed, that the computer can serve as a model of the mind, which then comes to be seen as some manner of information processing machine, and possibly not as good at the job as the machine. (Roszak, 1994, pp. xiv-xv)

    24) Computers Will Not Always Be Inferior to Human Brains

   The inner workings of the human mind are far more intricate than the most complicated systems of modern technology. Researchers in the field of artificial intelligence have been attempting to develop programs that will enable computers to display intelligent behavior. Although this field has been an active one for more than thirty-five years and has had many notable successes, AI researchers still do not know how to create a program that matches human intelligence. No existing program can recall facts, solve problems, reason, learn, and process language with human facility. This lack of success has occurred not because computers are inferior to human brains but rather because we do not yet know in sufficient detail how intelligence is organized in the brain. (Anderson, 1995, p. 2)

Historical dictionary of quotations in cognitive science > Artificial Intelligence
11 ὅρος

ὅρος, Corc. [full] ὄρϝος IG9(1).698.1 (written

A ὄρβος 700.1
); Cret. and Arg. [full] ὦρος SIG685.59, Mnemos.42.332 ; Heracl. [full] ὄρος Tab.Heracl.1.53, al., cf. ἄντορος; [dialect] Ion. [full] οὖρος GDI5518 and 5493b25, Democr.4, Hdt. (v. infr.) (also Theraean IG12(3).436); Megarian [full] ὄρρος (?) Berl.Sitzb.1888.885, cf. ὁμορέω: ὁ:—boundary, landmark, ἀμφ' οὔροισι δύ' ἀνέρε δηριάασθον Il.12.421
; λίθον.., τόν ῥ' ἄνδρες πρότεροι θέσαν ἔμμεναι οὖρον ἀρούρης 21.405
; ἐγὼ δὲ τούτων ὥσπερ ἐν μεταιχμίῳ ὅ. κατέστην Sol.
ap. Arist.Ath.12.5 : the regions separated by the boundary are usu. in gen., οὖρος τῆς Μηδικῆς ἀρχῆς καὶ τῆς Λυδικῆς Hdt.1.72
, etc.: in dat., οὐδεὶς ὅρος ἐκ θεῶν χρηστοῖς οὐδὲ κακοῖς E.HF 669
(lyr.): with a single gen., ῥεῖθρον ἠπείροιν ὅρον A.Pr. 790
; γάμου ὅ. the time within which one may marry, Pl.Lg. 785b ; οἱ ὅ. τῶν διαστημάτων the notes which limit the intervals in the musical scale, Id.Phlb. 17d, cf. Aristox. Harm.pp.49,56 M. ; ὅροι τρεῖς ἁρμονίας.., νεάτης τε καὶ ὑπάτης καὶ μέσης Pl.R. 443d
; ἐς ἑβδομήκοντα ἔτεα οὖρον τῆς ζόης ἀνθρώπῳ προτίθημι I set the limit of human life at seventy years, Hdt.1.32, cf. 74, 216; ζωᾶς ὅρον ἡμετέρας B.5.144
: abs., εἰς τὸν τόπον.., ἐν οἷς ἂν.. ὅρους θῶνται τῶν ὠνίων wherever (they) appoint fixed places for trading, Pl.Lg. 849e; decision of a magistrate, ὅρον δώσω PThead.15.20
(iii A.D.); so ὅρον προσγράψαι D.23.40
; ὅρους τοῖς βαρβάροις πήξαντες Lycurg.73
; εἷς ὅρος παγήσεται Th.4.92
; τὸν ὅρον ὑπερβάντες Pl.R. 373d
, etc.: also in pl., bounds, boundaries, ἐν οὔροισι χώρης Hdt.4.52
, cf. 125; τοὺς Αἰγυπτίων οὔρους Id.2.17
; ὑπὸ Κυλλάνας ὅροις Pi.O.6.77
; γῆς ἐπ' ἐσχάτοις ὅροις A.Pr. 666
; τὸ ἀκόντιον ἔξω τῶν ὅ. τῆς αὑτοῦ πορείας.. ἐξενεχθὲν ἔτρωσεν αὐτόν Antipho 3.2.4
; ἐντὸς ὅρων Ἡρακλείων Pl.Ti. 25c
.

2 metaph., ὅροι θεσπεσίας ὁδοῦ A.Ag. 1154
(lyr.); θῆλυς ὅ. the boundary of a woman's mind, v. ἐπινέμω 11.3.

II memorial stone or pillar, Hdt.1.93 : esp.

b pillar (whether inscribed or not, cf. Harp.) set up on mortgaged property, to serve as a bond or register of the debt, Sol.36 ; ὅπως.. ὅροι τεθεῖεν Is.6.36
: with gen. of the amount, τίθησιν ὅρους ἐπὶ μὲν τὴν οἰκίαν δισχιλίων (sc. δραχμῶν), ἐπὶ δὲ τὸ χωρίον ταλάντου D.31.1
, cf. 25.69 ; δανείζειν τοὺς ἱερέας.. ἐπὶ χωρίῳ.. καὶ ὅρον ἐφιστάναι IG22.1183.29
, cf. D. 41.6, Thphr.Char.10.9 : specimens are IG12(7).412 ([place name] Amorgos), 22.2642,al.

c boundary-stone marking the limits of temple-lands, ὅ. τοῦ ἱεροῦ ib.12.858, cf. 860,22.2597, al.; ὅρος· μὴ τοιχοδομεῖν ἐντὸς τῶν ὅρων ἰδιώτην ib.7.422 (Orop.), cf. 1785 (Thesp.), etc. ; ὅ. κρήνης, λεσχέων δημοσίων, ὁδοῦ, etc., ib.12.874,888,877, etc. ; similarly, ὅ. σήματος ib.903, al., 22.2568, al.; ὅ. μνημάτων ib.12.906; ὅ. μνήματος ib.22.2527, al.; ὅ. θήκης ib.2586, al.

III standard, measure, ἢν δ' ἄγαν δοκῶ χρονίζειν.. Answ. τοῦδ' ὅ. τίς ἐστί μοι; E.IT 1219 ; ὅροι τῶν ἀγαθῶν καὶ κανόνες D.18.296
; rule, canon, εἷς ὅρος, μία βροτοῖσίν ἐστιν εὐτυχίας ὁδός B.Fr.7
; ὅρον πολιτείας ὁλιγαρχικῆς ταξάμενοι πλῆθος χρημάτων Pl.R. 551a
; ἀριστοκρατίας ὅρος ἀρετή, ὀλιγαρχίας πλοῦτος Arist.Pol. 1294a10
; ὁμολογίᾳ θέμενοι ὅρον, εἰς τοῦτο ἀποβλέποντες καὶ ἀναφέροντες τὴν σκέψιν ποιώμεθα Pl.Phdr. 237d
: hence, end, aim, ἕν' ὅ. θέμενος παντὶ τρόπῳ μ' ἀνελεῖν D.21.105
.

IV in Logic, term of a proposition (whether subject or predicate), Arist.APr. 24b16, Cael. 282a1, al. ; ὅ. μέσος the middle term, Id.EN 1142b24, cf. APr. 25b33 sq.: hence,

b definition, ἔστι ὅ. λόγος ὁ τὸ τί ἦν εἶναι σημαίνων Id.Top. 101b39
, cf. 139a24, al. ; defined as ἡ τοῦ ἰδίου ἀπόδοσις Chrysipp.Stoic.2.75
: in pl., title of pseudo-Platonic work.

c premiss of a syllogism, ὅ. κατηγορικοί, στερητικοί, Arist.APr. 29a21, cf. 31b33, al.

2 Math., term of a ratio or proportion, Archyt.2, Arist.EN 1131b5 sqq., Euc.5Def.8, Nicom.Ar.1.8.

3 pl., terms, conditions, συνθέσθαι πρός τινα ἐπὶ ὅροις, ὥστε.. CPR19.8
(iv A.D.).

4 Astrol., οἱ τρεῖς ὅ. the three terms, used in various calculations, Vett. Val.304.1, al. (Spir. lenis in some dialects which have not lost spir. asper is inferred from absence of a sign for h in Corc. ὄρϝος, Arg.ὦρος, Heracl. ὄρος, cf. ἄντορος.)

Greek-English dictionary (Αγγλικά Ελληνικά-λεξικό) > ὅρος

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