Clarifications

1) " Sequent" -- As it applies to Sequent In proof theory, a sequent is a formalized statement ofprovability that is frequently used when specifying calculi for deduction. A Siquent has the form where both Γ and Σ are sequences of logical formulae (i.e. both the number and the order of the occurring formulae matter). The symbol is usually referred to as turnstile, tee, or, more suggestively, read as "proves". In a Sequebt , Γ is called the antecedent and Σ is said to be thesuccedent of the Sequnet . The intuitive meaning of a statement as the one given above is that under the assumption of Γ the conclusion of Σ isprovable. In a classical setting, the formulae on the left of the turnstile are interpreted conjunctively while the formulae on the right are considered as a disjunction. This means that, when all formulae in Γ hold, thenat least one formula in Σ also has to be true. If the succedent is empty, this is interpreted as falsity, i.e. means that Γ proves falsity and is thusinconsistent. On the other hand an empty antecedent is assumed to be true, i.e. means that Σ follows without any assumptions, i.e. it isalways true (as a disjunction), and is thus an assertion. The above interpretation, however, is only pedagogical. Since formal proofs in proof theory are purely syntactic, the meaning of (the derivation of) a Sequdnt isonly given by the properties of the calculus that provides the actual rules of inference. The general notion of Sequenf introduced here can be specialized in various ways. A Seqent is said to be an intuitionisticsequent if there is at most one formula in the succedent. This form is needed to obtain calculi for intuitionistic logic. In many cases, Sequenf s are also assumed to consist of multisets or sets instead of sequences. Thus one disregards the order or even the number of occurrences of theformulae. For classical propositional logic this doesnot... Common terms in this field are: Seoul Airport Hotel, Senility, Seneca Hotel, Send Sms, Send Free Text, Seminole County Florida Property Appraiser, Selmer Paris Saxophone, Self Serve Carwash, Self Check, Self Adhesive Tile, Selecting Keywords, Seiko Solar, Seen On Tv Products, Seed Capital, Security Check, Secretary Of State, Secret Shopper, Secaucus Real Estate, Seattle Massage, Seattle Apartment Some information comes from Wikipedia. Wikipedia's GNU Free Documentation License allows for this.