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Gödel's completeness theorem is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability in first-order logic.
In logic, more precisely in deductive reasoning, an argument is sound if it is both valid in form and its premises are true. Soundness also has a related meaning in mathematical logic, wherein logical systems are sound if and only if every formula that can be proved in the system is logically valid with respect to the semantics of the system.
A verb is a word that in syntax generally conveys an action, an occurrence, or a state of being. In the usual description of English, the basic form, with or without the particle to, is the infinitive. In many languages, verbs are inflected to encode tense, aspect, mood, and voice. A verb may also agree with the person, gender or number of some of its arguments, such as its subject, or object. Verbs have tenses: present, to indicate that an action is being carried out; past, to indicate that an action has been done; future, to indicate that an action will be done.
A fallacy is the use of invalid or otherwise faulty reasoning, or "wrong moves," in the construction of an argument, which may appear stronger than it really is if the fallacy is not spotted. The term was in the Western intellectual tradition introduced in the Aristotelian De Sophisticis Elenchis.
Deductive reasoning is the mental process of drawing deductive inferences. An inference is deductively valid if its conclusion follows logically from its premises, i.e. if it is impossible for the premises to be true and the conclusion to be false. For example, the inference from the premises "all men are mortal" and "Socrates is a man" to the conclusion "Socrates is mortal" is deductively valid. An argument is sound if it is valid and all its premises are true. Some theorists define deduction in terms of the intentions of the author: they have to intend for the premises to offer deductive support to the conclusion. With the help of this modification, it is possible to distinguish valid from invalid deductive reasoning: it is invalid if the author's belief about the deductive support is false, but even invalid deductive reasoning is a form of deductive reasoning.
In grammar, the term particle has a traditional meaning, as a part of speech that cannot be inflected, and a modern meaning, as a function word associated with another word or phrase, generally in order to impart meaning. Although a particle may have an intrinsic meaning, and indeed may fit into other grammatical categories, the fundamental idea of the particle is to add context to the sentence, expressing a mood or indicating a specific action. In English, for instance, the phrase "oh well" has no purpose in speech other than to convey a mood. The word 'up' would be a particle in the phrase to 'look up', implying that one researches something, rather than literally gazing skywards. Many languages use particles, in varying amounts and for varying reasons. In Hindi, for instance, they may be used as honorifics, or to indicate emphasis or negation. In some languages they are more clearly defined, such as Chinese, which has three types of zhùcí : Structural, Aspectual, and Modal. Structural particles are used for grammatical relations. Aspectual particles signal grammatical aspects. Modal particles express linguistic modality. Polynesian languages, which are almost devoid of inflection, use particles extensively to indicate mood, tense, and case.
The subjunctive is a grammatical mood, a feature of the utterance that indicates the speaker's attitude towards it. Subjunctive forms of verbs are typically used to express various states of unreality such as: wish, emotion, possibility, judgment, opinion, obligation, or action that has not yet occurred; the precise situations in which they are used vary from language to language. The subjunctive is one of the irrealis moods, which refer to what is not necessarily real. It is often contrasted with the indicative, a realis mood which is used principally to indicate that something is a statement of fact.
In grammar, a future tense is a verb form that generally marks the event described by the verb as not having happened yet, but expected to happen in the future. An example of a future tense form is the French aimera, meaning "will love", derived from the verb aimer ("love"). The "future" expressed by the future tense usually means the future relative to the moment of speaking, although in contexts where relative tense is used it may mean the future relative to some other point in time under consideration.
Metalogic is the study of the metatheory of logic. Whereas logic studies how logical systems can be used to construct valid and sound arguments, metalogic studies the properties of logical systems. Logic concerns the truths that may be derived using a logical system; metalogic concerns the truths that may be derived about the languages and systems that are used to express truths.
Inductive reasoning is a method of reasoning in which a body of observations is considered to derive a general principle. It consists of making broad generalizations based on specific observations. Inductive reasoning is distinct from deductive reasoning. If the premises are correct, the conclusion of a deductive argument is certain; in contrast, the truth of the conclusion of an inductive argument is probable, based upon the evidence given.
A formal system is an abstract structure used for inferring theorems from axioms according to a set of rules. These rules, which are used for carrying out the inference of theorems from axioms, are the logical calculus of the formal system. A formal system is essentially an "axiomatic system".
The English modal verbs are a subset of the English auxiliary verbs used mostly to express modality. They can be distinguished from other verbs by their defectiveness and by their neutralization.
A modal verb is a type of verb that contextually indicates a modality such as a likelihood, ability, permission, request, capacity, suggestion, order, obligation, or advice. Modal verbs always accompany the base (infinitive) form of another verb having semantic content. In English, the modal verbs commonly used are can, could, may, might, shall, should, will, would, ought to, used to, dare and must.
A realis mood is a grammatical mood which is used principally to indicate that something is a statement of fact; in other words, to express what the speaker considers to be a known state of affairs, as in declarative sentences. Most languages have a single realis mood called the indicative mood, although some languages have additional realis moods, for example to express different levels of certainty. By contrast, an irrealis mood is used to express something that is not known to be the case in reality.
In linguistics, irrealis moods are the main set of grammatical moods that indicate that a certain situation or action is not known to have happened at the moment the speaker is talking. This contrasts with the realis moods.
Epistemic modality is a sub-type of linguistic modality that encompasses knowledge, belief, or credence in a proposition. Epistemic modality is exemplified by the English modals may, might, must. However, it occurs cross-linguistically, encoded in a wide variety of lexical items and grammatical structures. Epistemic modality has been studied from many perspectives within linguistics and philosophy. It is one of the most studied phenomena in formal semantics.
An argument is a statement or group of statements called premises intended to determine the degree of truth or acceptability of another statement called conclusion. Arguments can be studied from three main perspectives: the logical, the dialectical and the rhetorical perspective.
In linguistics, grammatical mood is a grammatical feature of verbs, used for signaling modality. That is, it is the use of verbal inflections that allow speakers to express their attitude toward what they are saying. The term is also used more broadly to describe the syntactic expression of modality – that is, the use of verb phrases that do not involve inflection of the verb itself.
Tense–aspect–mood or tense–modality–aspect is a group of grammatical categories that are important to understanding spoken or written content, and which are marked in different ways by different languages.
Yatzachi Zapotec is an Oto-Manguean language of the Zapotecan branch, spoken in northern central Oaxaca, Mexico. 2,500 self-reported being Yatzachi speakers for the 1990 Mexican census, but the actual number of speakers is unknown. The Yatzachi dialect belongs to the Villa Alta group of Zapotec dialects, of which the main dialect is San Bartolomé Zoogocho. The degree of mutual intelligibility between Yatzachi and the San Bartolomé Zoogocho dialect is estimated to be around 90 percent.
References
- ↑ Loos, Eugene E.; Susan Anderson; Dwight H. Day, Jr; Paul C. Jordan; J. Douglas Wingate. "What is deductive mood?". Glossary of linguistic terms. SIL International. Retrieved 2022-09-13.
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