entail

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(ĕn-tāl', ĭn-) pronunciation
tr.v., -tailed, -tail·ing, -tails.
  1. To have, impose, or require as a necessary accompaniment or consequence: The investment entailed a high risk. The proposition X is a rose entails the proposition X is a flower because all roses are flowers.
  2. To limit the inheritance of (property) to a specified succession of heirs.
  3. To bestow or impose on a person or a specified succession of heirs.
n.
    1. The act of entailing, especially property.
    2. The state of being entailed.
  1. An entailed estate.
  2. A predetermined order of succession, as to an estate or to an office.
  3. Something transmitted as if by unalterable inheritance.

[Middle English entaillen, to limit inheritance to specific heirs : en-, intensive pref.; see en-1 + taille, tail; see tail2.]

entailment en·tail'ment n.

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verb

  1. To have as an accompaniment, a condition, or a consequence: carry, involve. See start/end.
  2. To have as a need or prerequisite: ask, call for, demand, involve, necessitate, require, take. See necessary/unnecessary, over/under.


v

Definition: require
Antonyms: exclude, leave out

The growth of landed estates in England from the mid-16th cent. until the 1880s was partly a product of the system of ‘entailing’ property. Until the mid-17th cent., the available forms of entail were restricted, but thereafter the courts agreed to permit an owner to tie up his estate to the second and third generation, through a process of ‘contingent remainders’. It was once held that as a result great estates were kept together, but modern research holds that the system of entailing property was introduced partly to protect the financial interests of younger children, that entailed estates could be partially or completely freed, and that the consolidation of estates was due to factors other than entail.

The relationship between a set of premises and a conclusion when the conclusion follows from the premises, or may validly be inferred from the premises. Many philosophers identify this with it being logically impossible that the premises should all be true, yet the conclusion false. Others are sufficiently impressed by the paradoxes of strict implication to look for a stronger relation, which would distinguish between valid and invalid arguments within the sphere of necessary propositions. The search for a stronger notion is the field of relevance logics.

This is the name given to the legal status of a landed estate when its ownership is restricted through inheritance to biological descendants of the original grantee in order to maintain its size. Originally practiced in New York and the South, entail was abolished, along with primogeniture (inheritance by only the eldest son), throughout the United States before 1800. The practice of protecting large estates through restrictions on inheritance was brought from England, but owing to the vast abundance of available rich land in America, workers and tenants could obtain their own land, and large holdings became less profitable. Also, descendants of landowners could turn to the challenge of earning even greater wealth through their own efforts, and inheritance of large holdings was no longer the major path to wealth.

Abolition of entail and primogeniture was part of a general reform movement that included the grant to married women of the right to control their own property and the disestablishment of churches.

See also Primogeniture.


entail, in law, restriction of inheritance to a limited class of descendants for at least several generations. The object of entail is to preserve large estates in land from the disintegration that is caused by equal inheritance by all the heirs and by the ordinary right of free alienation (disposal) of property interests. Legal devices similar to entail were known in Roman law and in all the countries of Europe. In England the entail became common in the early 13th cent., and in its most usual form was a conveyance by a grantor (owner) of real property to a grantee and the "heirs of his body," i.e., his lawful offspring, in successive generations. In the inheritance the rule of primogeniture was observed. The subsequent development of the entail reflects a continuing struggle between the effort to preserve large estates and the need for free alienation. By the mid-13th cent. the courts interpreted the birth of a live baby as the satisfaction of a condition that vested the grantee with the power of alienation. This result was overcome by the statute De donis conditionalibus [conditional gifts] (1285), which gave effect to the grantor's intent. In time the grantee was able to get control of the property despite the statutory prohibition by use of the fine and other technical legal devices. Current English law permits the holder of entailed property (either real or personal) to dispose of it by deed; otherwise the entail persists. In the United States for the most part entails are either altogether prohibited or limited to a single generation.


This entry contains information applicable to United States law only.

To abridge, settle, or limit succession to real property. An estate whose succession is limited to certain people rather than being passed to all heirs.

In real property, a fee tail is the conveyance of land subject to certain limitations or restrictions, namely, that it may only descend to certain specified heirs.

The relation that holds between one or more propositions P1 ... Pn and each proposition C which follows logically from them. Thus P1 ... Pn entail C (frequently symbolized P1 ... Pn C) if, and only if, the inference from P1 ... Pn to C is logically valid. The further analysis of this relation has been extensively discussed and disputed both by logicians and by philosophers. It is generally agreed that whenever A entails B it must be impossible for A to be true without B also being true, in which case, according to the definition introduced by C. I. Lewis, A strictly implies B. The further analysis of entailment has thus come to be linked to the account given of the logic of the modal notions of possibility and necessity which is supplied in works on modal logic. Lewis, who produced the first axiomatized modal logic, proposed that the relation of strict implication should be regarded as the correct formal counterpart of the informal notion of entailment. Others, however, for example Anderson and Belnap, have argued that for A to entail B it is not sufficient merely that it be impossible for A to be true without B being true. On their view there must also be some connection between the meanings of A and B, and the truth of A must be relevant to the truth of B (giving rise to the idea of developing what has been called a relevance logic). This would mean, for example, insisting that although a contradiction strictly implies any proposition whatsoever ('Grass is green and grass is not green' strictly implies 'The earth is flat') it only entails those propositions to which it is relevant ('Grass is green and grass is not green' entails 'Grass is not red').

(Published 1987)

— Mary Elizabeth Tiles

    Bibliography
  • Anderson, A. R., and Belnap, N. D. Jr. (1975). Entailment, vol. i.
  • Hughes, G. E., and Cresswell, M. J. (1968). An Introduction to Modal Logic.
  • Lewis, C. I. (1922). 'Implication and the algebra of logic'. Mind 21.


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pronunciation

IN BRIEF: To involve.

pronunciation The project will entail much in-depth research and an oral report.

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Note: for some discussion of the notation  \models , and  \vdash see below.

In logic, entailment is a relation between a set of sentences (e.g.,[1] meaningfully declarative sentences or truthbearers) and a sentence. Let Γ be a set of one or more sentences; let S1 be the conjunction of the elements of Γ, and let S2 be a sentence: then, Γ entails S2 if and only if S1 and not-S2 are logically inconsistent. S2 is called a logical consequence of Γ; S1 is said to logically imply S2.

Two sentences are inconsistent if and only if they cannot both be true; they are logically inconsistent if and only if they are inconsistent as a result of their logical form.

Thus if

Γ = {“Roses are red”, “Violets are blue”},
S1 = “Roses are red and Violets are blue”

and

S2 = “Violets are Blue”

then Γ entails S2, because

“Roses are red and Violets are blue”

and

“Violets are not blue”

are logically inconsistent. They are logically inconsistent in that their logical form assures that they cannot be both true, their logical forms being p and q and not-q.

On the other hand if

Γ = {“John is a bachelor”},
S1 = “John is a bachelor” and
S2 = “John is a man”

then Γ does not entail S2 because

S1, “John is a bachelor”

and

(not)S2, “John is not a man”

then they may be inconsistent (given that a bachelor is necessarily a man), yet they are not logically inconsistent, which is to say, their logical form p and not-q is not the reason for their inconsistency.

Contents

Logical form

Given Γ is a set of one or more declarative sentences.

Since

  • Γ entails S2 if and only if S1 and not-S2 are logically inconsistent

and

  • S1 and not-S2 are logically inconsistent if they are inconsistent as a result of their logical forms

it follows that

  • Γ entails S2 if and only if S1 and not-S2 are inconsistent as a result of their logical forms.

It is therefore of the first importance to clarify the term logical form and explain how the logically relevant form(s)[2] of a sentence can be established.

The logical form of sentences can be revealed by means of a formal language enabling the following definition of entailment. Roughly, if S1 and S2 are interpretations of two sentences θ and ψ in a formal language of classical logic, then S1 entails S2 if and only if not (θ and not ψ) is true under all interpretations.

More precisely, if Γ is a set of one or more sentences and S1 is the conjunction of the elements of Γ and S2 is a sentence, Γ entails S2 if and only if not (S1 and not-S2) is a logical truth. S2 is called the 'logical consequent' of Γ. S1 is said to 'logically imply' S2.

Not (S1 and not-S2) is a logical truth if θ and Ψ are closed well-formed formulae (often denoted 'wff'), wffs (sentences) in a formal language L in classical logic, and I is an interpretation of L, and θ is true under I if and only if S1 and Ψ is true under I if and only if S2, and not (θ and not Ψ) is logically valid.

A closed wff Φ in L is 'logically valid' if and only if Φ is true under all interpretations of L. Hence

Thus if Γ = {“Roses are red”, “Violets are blue”}, S1=“Roses are red and Violets are blue” and S2 = “Violets are Blue” then Γ entails S2 because not(S1 and not-S2), “It is not the case that roses are red and violets are blue and violets are not blue” is a logical truth.

Not(S1 and not-S2) is a logical truth because there are two closed wfs, P&Q and Q in a formal language L in classical logic and there is an interpretation I of L, and P&Q is true under I if and only if roses are red and violets are blue, and Q is true under I if and only if violets are blue, and ¬((P&Q)&¬Q) is logically valid. ¬((P&Q)&¬Q)) is logically valid because it is true under all interpretations of L (note that ¬ means not).

It will be noted that, on these definitions, if (i) S1 is inconsistent (self-contradictory) or (ii) not-S2 is inconsistent (self-contradictory) then (S1 and not-S2) is inconsistent (not consistent) and hence S1 entails S2.

Proof procedures, and relationship between entailment and deduction

It is of considerable interest to be able to prove that Γ entails S2 and hence that Γ/S2 is a valid argument. Ideally, entailment and deduction would be extensionally equivalent. However, this is not always the case. In such a case, it is useful to break the equivalence down into its two parts:

A deductive system S is complete for a language L if and only if A \models_L X implies A \vdash_S X: that is, if all valid arguments are deducible (or provable), where \vdash_S denotes the deducibility relation for the system S. NB A \models_L X means that X is a semantic consequence of A in the language L, and A \vdash_S X means that X is provable from A in the system S.

A deductive system S is sound for a language L if and only if A \vdash_S X implies A \models_L X: that is, if no invalid arguments are provable.

Many introductory textbooks (e.g. Mendelson's "Introduction to Mathematical Logic") that introduce first-order logic, include a complete and sound inference system for the first-order logic. In contrast, second-order logic — which allows quantification over predicates — does not have a complete and sound inference system with respect to a full Henkin (or standard) semantics.

Proof of entailment

Since

a proof that not (θ and not Ψ) is logically valid would be a proof that Γ entails S2.

It can be easily demonstrated, for example by means of a truth-table, that ¬((P & Q) & ¬Q) is a tautology and hence true under all interpretations and hence logically valid. Moreover, if T is a consistent theory in L and ¬(θ ∧ ¬Ψ) is a theorem in T (written ⊢T¬(θ ∧ ¬Ψ)) then ¬(θ ∧ ¬Ψ) is logically valid and, consequently, all interpretations of ¬(θ ∧ ¬Ψ) are logical truths, including not(S1 and not-S2). Hence Γ entails S2 if ⊢T¬(θ ∧ ¬Ψ) and T is consistent.

Relationship to other terms

Entailment is one of a number of inter-related terms of logical appraisal. Its relationship to other such terms includes the following see e.g. Strawson (1952)[3] Section 13, 'Entailment and Inconsistency', pp 19 et seq) where S1 and S2 are sentences, or S1 is the conjunction of all the sentences in some set of sentences Γ, S1 entails S2 if and only if:

  1. S1 and not-S2 are inconsistent (not consistent)
  2. (S1 and not-S2) is logically impossible
  3. Not(S1 and not-S2) is logically true
  4. Not(S1 and not-S2) is necessarily true
  5. (S1 and not-S2) is logically false
  6. S1 is a sufficient condition for S2
  7. S2 is a necessary condition for S1
  8. It would be self-contradictory to affirm S1 and deny S2
  9. An argument whose premise is S1 and conclusion is S2 is a valid argument
  10. If S1 and S2 are interpretations of two sentences θ and ψ in a formal language of classical logic (elementary logic), then S1 entails S2 if and only if not (θ and ¬ψ) is true in all interpretations.

Syntactic consequence

A formula A is a syntactic consequence[4][5][6][7] within some formal system FS of a set Г of formulas if there is a formal proof in FS of A from the set Г.

\Gamma \vdash_{\mathrm FS} A

Syntactic consequence does not depend on any interpretation of the formal system.[8]

Semantic consequence

A formula A is a semantic consequence of a set of statements Г

\Gamma \models A,

if and only if no interpretation \mathcal{I} makes all members of Г true and A false.[9] Or, in other words, the set of the interpretations that make all members of Г true is a subset of the set of the interpretations that make A true.

Entailment vs material implication

The difference between material implication and entailment is that they apply in different contexts. The first is a statement of logic, the second of metalogic. If p and q are two sentences then the difference between "p implies q" and "p is a proof of q" is that the first is a statement within formal logic, the second is a statement about it. Entailment is a concept of proof theory, whereas material implication is the mechanics of a proof.[10]

Limitations

Entailment is one form but not the only form of inference. Inductive reasoning is another. Scientific method involves inferences that are not solely entailment. Entailment does not encompass non-monotonic reasoning or defeasible reasoning. See also

Modal accounts

Modal accounts of logical consequence are variations on the following basic idea:

  • Γ \vdashA just in case it is necessary that if all of the elements of Γ are true, then A is true.

Alternatively (and, most would say, equivalently):

  • Γ \vdashA just in case it is impossible for all of the elements of Γ to be true and A false.

Such accounts are called "modal" because they appeal to the modal notions of necessity and (im)possibility. 'It is necessary that' is often cashed out as a universal quantifier over possible worlds, so that the accounts above translate as:

  • Γ \vdashA just in case there is no possible world at which all of the elements of Γ are true and A is false (untrue).

Consider the modal account in terms of the argument given as an example above:

All frogs are green.
Kermit is a frog.
Therefore, Kermit is green.

The conclusion is a logical consequence of the premises because we can't imagine a possible world where (a) all frogs are green; (b) Kermit is a frog; and (c) Kermit is not green.

Modal-formal accounts

Modal-formal accounts of logical consequence combine the modal and formal accounts above, yielding variations on the following basic idea:

  • Γ \vdashA just in case it is impossible for an argument with the same logical form as Γ/A to have true premises and a false conclusion.

Most logicians would probably agree that logical consequence, as we intuitively understand it, has both a modal and a formal aspect, and that some version of the modal/formal account is therefore closest to being correct.

Warrant-based accounts

The accounts considered above are all "truth-preservational," in that they all assume that the characteristic feature of a good inference is that it never allows one to move from true premises to an untrue conclusion. As an alternative, some have proposed "warrant-preservational" accounts, according to which the characteristic feature of a good inference is that it never allows one to move from justifiably assertible premises to a conclusion that is not justifiably assertible. This is (roughly) the account favored by intuitionists such as Michael Dummett.

Non-monotonic logical consequence

The accounts discussed above all yield monotonic consequence relations, i.e. ones such that if A is a consequence of Γ, then A is a consequence of any superset of Γ. It is also possible to specify non-monotonic consequence relations to capture the idea that, e.g., 'Tweety can fly' is a logical consequence of

{Birds can typically fly, Tweety is a bird}

but not of

{Birds can typically fly, Tweety is a bird, Tweety is a penguin}.

For more on this, see belief revision#Non-monotonic inference relation.

Philosophical issues

  • The literature is ambiguous regarding precisely what 'logical implication' means. Sometimes it is taken to be a pretheoretic notion capable of definition in several ways, usually involving modality and stated something like "A set of sentences logically implies a sentence A if and only if it is impossible that all the members of the set be true while A false". Other times it is taken as the definition given in the introduction to this article, perhaps as a replacement for the pretheoretic notion itself. This often occurs in the sciences and mathematics; that is, intuitive notions get replaced by more precise, rigorously defined ones. E.g., in mathematics, many now take 'computable' in the sense of 'effectively calculable' to be 'computable' in the sense of Turing, Church, Gödel, Herbrand, or Post.[11]

It is impossible to state rigorously the definition of 'logical implication' as it is understood pretheoretically, but many have taken the Tarskian model-theoretic account as a replacement for it. Some, e.g. Etchemendy 1990, have argued that they do not coincide, not even if they happen to be co-extensional (which Etchemendy believes they are not). This debate has received some recent attention. See "The Blackwell Guide to Philosophical Logic",[12] for a good introduction to it.

  • It is often thought that a peculiar feature of logical implication is that a contradiction implies anything and that anything implies a validity. For example, 'Abraham Lincoln was president of the US' implies '2+2=4', and 'the white dot is black' implies 'the integer 25 is greater than the integer 30'. The peculiarity in these examples is oft-attributed to a lack of relevance between the two sentences. A formal notion of relevance has been characterized by relevant logic and applied to the notion of logical implication in the seminal work of Anderson & Belnap 1975. Another property they argue that implication should have is necessity. Thus A implies B only if it is necessary that A implies B. This feature of implication is lacking in the usual model-theoretic definition (i.e. the one given in the introduction).
  • Some logicians[who?] draw a firm distinction between the conditional connective (the syntactic sign "→"), and the implication relation (the formal object denoted by the double arrow symbol "⇒"). These logicians use the phrase not p or q for the conditional connective and the term implies for the implication relation. Some explain the difference by saying that the conditional is the contemplated relation while the implication is the asserted relation.[citation needed] In most fields of mathematics, it is treated as a variation in the usage of the single sign "⇒", not requiring two separate signs. Not all of those who use the sign "→" for the conditional connective regard it as a sign that denotes any kind of object, but treat it as a so-called syncategorematic sign, that is, a sign with a purely syntactic function. For the sake of clarity and simplicity in the present introduction, it is convenient to use the two-sign notation, but allow the sign "→" to denote the boolean function that is associated with the truth table of the material conditional. These considerations result in the following scheme of notation.
\begin{matrix}
p \rightarrow q & \quad & \quad & p \Rightarrow q \\
\mbox{not}\ p \ \mbox{or}\ q & \quad & \quad & p \ \mbox{implies}\ q
\end{matrix}

See also

Notes

  1. ^ It should be noted that entailment can be employed in sentences which are not necessarily truthbearers, but also to express contingencies in alethic modalities: imagined situations, evocative situations, or in situations involving necessity, duty, or the law.
  2. ^ We should not assume that a sentence has just one logical form. If T1 ="If Greeks are men and men are mortal then Greeks are men", we could say that the logical form of T1 is "IF P and Q THEN P", and thus the logical form of ."Greeks are men" is "P". If T2 is ="If Greeks are men and men are mortal then Greeks are mortal", we could say that the logical from of T2 is "If all A is B and all B is C then all A is C", and thus the logical form of "Greeks are men" is "All A is B". Hence we cannot say that THE logical form of "Greeks are men" is "P" nor "All A is B".
  3. ^ Strawson, P.F. (1952), Introduction to Logical Theory, Methuen 
  4. ^ Dummett, Michael (1993) Frege: philosophy of language Harvard University Press, p.82ff
  5. ^ Lear, Jonathan (1986) Aristotle and Logical Theory Cambridge University Press, 136p.
  6. ^ Creath, Richard, and Friedman, Michael (2007) The Cambridge companion to Carnap Cambridge University Press, 371p.
  7. ^ FOLDOC: "syntactic consequence"
  8. ^ Hunter, Geoffrey, Metalogic: An Introduction to the Metatheory of Standard First-Order Logic, University of California Pres, 1971, p. 75.
  9. ^ The Cambridge Dictionary of Philosophy
  10. ^ Michael Huth, Mark Ryan: Logic in Computer Science; Cambridge University Press; p. 37
  11. ^ See for example Davis 1965
  12. ^ Goble 2001 Chapter 6

Resources

  • Anderson, A.R.; Belnap, N.D., Jr. (1975), Entailment, 1, Princeton, NJ: Princeton .
  • Barwise, Jon; Etchemendy, John (2008), Language, Proof and Logic, Stanford: CSLI Publications .
  • Brown, Frank Markham (2003), Boolean Reasoning: The Logic of Boolean Equations  1st edition, Kluwer Academic Publishers, Norwell, MA. 2nd edition, Dover Publications, Mineola, NY, 2003.
  • Davis, Martin, (editor) (1965), The Undecidable, Basic Papers on Undecidable Propositions, Unsolvable Problems And Computable Functions, New York: Raven Press . Papers include those by Gödel, Church, Rosser, Kleene, and Post.
  • Dummett, Michael (1991), The Logical Basis of Metaphysics, Harvard University Press .
  • Edgington, Dorothy (2001), Conditionals, Blackwell  in Lou Goble (ed.), The Blackwell Guide to Philosophical Logic.
  • Edgington, Dorothy (2006), Conditionals, http://plato.stanford.edu/entries/conditionals  in Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy.
  • Etchemendy, John (1990), The Concept of Logical Consequence, Harvard University Press .
  • Goble, Lou, ed. (2001), The Blackwell Guide to Philosophical Logic, Blackwell .
  • Hanson, William H (1997), "The concept of logical consequence", The Philosophical Review 106  365–409.
  • Hendricks, Vincent F. (2005), Thought 2 Talk: A Crash Course in Reflection and Expression, New York: Automatic Press / VIP, ISBN 87-991013-7-8 
  • Planchette, P. A. (2001), Logical Consequence  in Goble, Lou, ed., The Blackwell Guide to Philosophical Logic. Blackwell.
  • Quine, W.V. (1982), Methods of Logic, Cambridge, MA: Harvard University Press  (1st ed. 1950), (2nd ed. 1959), (3rd ed. 1972), (4th edition, 1982).
  • Shapiro, Stewart (2002), Necessity, meaning, and rationality: the notion of logical consequence  in D. Jacquette, ed., A Companion to Philosophical Logic. Blackwell.
  • Tarski, Alfred (1936), On the concept of logical consequence  Reprinted in Tarski, A., 1983. Logic, Semantics, Metamathematics, 2nd ed. Oxford University Press. Originally published in Polish and German.
  • A paper on 'implication' from math.niu.edu, Implication
  • A definition of 'implicant' AllWords

External links


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Dansk (Danish)
v. tr. - medføre, indebære, fastlægge arvefølge til, belægge med arveregler, tildele umisteligt
n. - stamgods, fideikommis, arvegang

Nederlands (Dutch)
vestigen op, opleggen, iets tot erfgoed maken, met zich meebrengen, erfenis

Français (French)
v. tr. - entraîner, occasionner, comporter (un risque), imposer (une souffrance), (Jur) substituer (un héritage)
n. - entraînement, résultat

Deutsch (German)
v. - mit sich bringen
n. - Umwandlung

Ελληνική (Greek)
v. - συνεπάγομαι, (συν)επιφέρω

Italiano (Italian)
assegnare, implicare

Português (Portuguese)
v. - vincular (bens) (Jur.), legar, causar obrigatoriamente

Русский (Russian)
влечь за собой, навлекать

Español (Spanish)
v. tr. - traer consigo, acarrear, suponer, implicar
n. - vinculación, vínculo

Svenska (Swedish)
v. - medföra, vara förenad med

中文(简体)(Chinese (Simplified))
使必需, 使承担, 使蒙受, 限定继承权

中文(繁體)(Chinese (Traditional))
v. tr. - 使必需, 使承擔, 使蒙受
n. - 限定繼承權

한국어 (Korean)
v. tr. - 남기다, 필요로 하다, 한정 상속을 하다
n. - 한사 상속, 숙명적 유전, 계승 예정 순위

日本語 (Japanese)
n. - 限嗣相続
v. - 伴う, 必要とする, 課す, 限嗣相続させる

العربيه (Arabic)
‏(فعل) يستلزم‏

עברית (Hebrew)
v. tr. - ‮גרר, הצריך, דרש, הנחיל, הוריש, חייב‬
n. - ‮ירושה, עיזבון, הורשה, חווה שעברה בירושה‬


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