According to Definition 3-16, we have 3 ? IIF( 1 ) ? RCS\{?} and, with Theorem 3-25, Therefore ? = ?)}. Thus we have AVAS( 3 ) = AVAS( 1 ), ? = ? ? (? ? ?) ? AVP( 2 ) ? AVP( 3 ) and ? = ? ? ,
Suppose Dom() = 0. Then we have = ? = [?*, ?, ] and thus ,
Dom()-1) and Definition 3-18, we have that ? AF ,
i )]), because, if not, we would have ? ? STSEQ() or ? = ?, which contradicts the hypothesis and Postulate 1-1 respectively. With a), it holds that f ,
with which + is then in each case the desired RCS-element. In order to ease the treatment of, we will now first show that g) If + ? CdIF(*) ? NIF(*) ? PEF(*), then ? CdIF(Dom()-1) ? NIF(Dom()-1) ? PEF ,
According to Definition 3-15 and with c), d) and f), there are then ? ,
Then we can make an exclusion assumption that allows us to determine Dom(AVS( + )) for all other cases just with c), g) and Theorem, pp.3-25 ,
Suppose ? CdIF(Dom()-1) According to Definition 3-2, there is then an i ? Dom(AVAS(Dom()-1)) such that there is no l ? ,
According to Definition 3-15, there are then ?, p.where FV ,
According to Theorem 3-28, we then have AVAP() = AVAP(Dom()-1) We can distinguish 13 subcases According to Definition 3-3, NIF, issue.11 ,
-1 such that B ? ? is available in Dom()-1 at j and B ? C() is available in Dom( ,
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where FV(?) ? {?}, such that ,
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The set of expressions (EXP; metavariables: ?, ? ,
The set of terms (TERM; metavariables: ?, ?, p.13 ,
The set of formulas (FORM, p.13 ,
Assignment of the set of variables that occur free in a term ? or in a formula ? (FV), p.22 ,
The set of closed formulas (CFORM), p.23 ,
The set of sentences (SENT; metavariables: ?, p.23 ,
The set of proper expressions (PEXP), p.24 ,
The set of sentence sequences (SEQ), p.25 ,
Assignment of the set of subterms of the members of a sequence (STSEQ), p.26 ,
Assignment of the set of subterms of the elements of a set of formulas X (STSF), p.26 ,
Substitution of closed terms for atomic terms in terms, formulas, sentences and sentence sequences, p.27 ,
Assignment of the set of segments of (SG), p.50 ,
Suitable sequences of natural numbers for subsets of sentence sequences, p.55 ,
Segment sequences for sentence sequences, p.58 ,
Assignment of the set of segment sequences for (, p.58 ,
AS?comprising segment sequence for a segment, p.61 ,
Assignment of the set of AS?comprising segment sequences in (ASCS), p.61 ,
Availability of a proposition in a sentence sequence at a position, p.104 ,
Availability of a proposition in a sentence sequence, p.105 ,
Assignment of the set of available sentences (AVS), p.105 ,
Assignment of the set of available assumption?sentences (AVAS), p.105 ,
Assignment of the set of available propositions (AVP), p.105 ,
Assignment of the set of available assumptions (AVAP), p.105 ,
The set of rule?compliant sentence sequences (RCS), p.135 ,
The closure of a set of propositions under deductive consequence, p.142 ,
Term denotation functions for models and parameter assignments, p.218 ,
Satisfaction functions for models and parameter assignments, p.220 ,
The closure of a set of propositions under model?theoretic consequence, p.234 ,
Correctness of the Speech Act Calculus relative to the model?theory, p.250 ,
?models and their L?restrictions behave in the same way with regard to, p.253 ,
A set of L?propositions is L H ?satisfiable if and only if it is, p.253 ,
L?sequences are RCS H ?elements if and only if they are RCS?elements, p.254 ,
An L?proposition is L H ?derivable from a set of L?propositions if and only if it is L?derivable from that set, p.254 ,
A set of L?propositions is L H ?consistent if and only if it is, p.255 ,
Rule of Conditional Introduction (CdI), p.123 ,
Rule of Conditional Elimination (CdE), p.124 ,
Rule of Conjunction Introduction (CI), p.124 ,
Rule of Biconditional Introduction (BI), p.124 ,
Rule of Negation Introduction (NI), p.125 ,
Rule of Particular?quantifier Introduction (PI), p.126 ,
Rule of Particular?quantifier Elimination (PE), p.126 ,
Rule of Identity Introduction (II), p.126 ,