************************** * Round 29 * * Theme: Logic * * Judge: Oerjan Johansen * * Wizard: Doug R. Steen * ************************** The Winner and next Judge is: Stein Kulseth The Wizard is: Stein Kulseth ==== Style Points ==== Wizard Doug R. Steen 0.5 Jeremy D. Selengut 0 Joshua Howard 0 Peter Sarrett -1 Ronald Kunne 1 Stein Kulseth 3.5 Stephen Turner 1.5 Vanyel -2.5 **** Holiday Break Overrule: ==== R.O. overrule 29:a. The FRC will take a Christmas break from Friday December 16th 1994 0:01 Norwegian time (Thursday December 15th 1994 23:01 GMT) until Friday January 6th 1995 0:01 Norwegian time (Thursday January 5th 1995 23:01 GMT). Any actions carried out during this time will be deemed to have no effect on the FRC, even if they were done before this R.O. overrule came into force: for example any rules or calls for votes posted during this time will be ignored. All periods of time mentioned in the R.O.s, except those relating to the length of votes on R.O. overrules, will be measured ignoring the time during the break. ==== FOR: Stephen Turner Stein Kulseth Vanyel Joshua Howard Wizard Dug Doug Chatham Storm Oerjan Johansen ==== AGAINST: Peter Sarrett Ronald Kunne **** List of Rules (All times are Norwegian time, GMT+1) **** Fantasy Rule 29:1 Wizard Doug R. Steen, Mon Dec 12 08:39:09 1994 VALID, 1/2 Point ==== FAxiom 29.1.1: All valid fantasy rules this round will contain _only_ a list of uniquely labeled Fantasy Statements (FStatements) which are consistent with the FStatements from previous valid fantasy rules. FAxiom 29.1.2: All FStatements will have exactly _one_ FValue. FAxiom 29.1.3: Any FStatement which is not demonstrated to have a certain FValue does _not_ have that FValue. FAxiom 29.1.4: FAxioms, FLemmas, FTheorems, and FMethods are all FStatements. FAxiom 29.1.5: Frue (F) and Talse (T) are FValues. FMethod 29.1.1: If an FStatement starts with the same three words as an FStatement which is known to be Frue, then it too is Frue. **** Fantasy Rule 29:2 Peter Sarrett, Mon Dec 12 10:19:18 1994 VALID, -1/2 Point ==== FAxiom 29.2.1: FStatements which assign values to themselves, other statements, or other classes, categories, or types of statements must be FMethods. Nothing else may be an FMethod, and FMethods may be nothing else. FAxiom 29.2.2: FStatements which define, restrict, or otherwise relate to the form or construction of FLogic (including the definition of terms) must be FAxioms. Nothing else may be an FAxiom, and FAxioms may be nothing else. **** Fantasy Rule 29:3 Peter Sarrett, Mon Dec 12 11:44:24 1994 VALID, -1/2 Point ==== FAxiom 29.3.1: FVariables are any symbols used to represent FValues. FAxiom 29.3.2: FOperations are processes involving the change, manipulation, or evaluation of FValues (or the FVariables representing them). FOperations evaluate to an FValue, called the FResult. FAxiom 29.3.3: FOperands are symbols used to represent FOperations. FAxiom 29.3.4: FValues must be declared in an FAxiom before they may be used in other FStatements. Stating that something is an FValue declares that FValue. FAxiom 29.3.5: FOperands must be defined in an FAxiom before they may be used in other FStatements. Defining an FOperand consists of naming the FOperation that FOperand performs, providing a symbol for the FOperand, and defining the FOperation. FAxiom 29.3.6: FOperations must be defined in an FAxiom before they may be used in other FStatements. Defining an FOperation consists of providing a format or series of formats showing how the operation is used, and providing a set of FResults and/or an English description such that for all possible FValues to which the FOperation might be applied, the resulting FResults can be determined. FAxiom 29.3.7: Floyd is an FValue. FMethod 29.3.1: All FAxioms have an FValue of Floyd. **** Fantasy Rule 29:4 Vanyel, Mon Dec 12 17:21:53 1994 INVALID, -1.5 Point ==== FAxiom 29.4.1: FP and FQ are FVariables. FAxiom 29.4.2: Frue, Talse, and Floyd are the only valid FValues, and may be abbreviated as follows: Frue Fr Talse Ta Floyd Fl FMethod 29.4.3: Only Axioms may have the FValue "Floyd". FAxiom 29.4.4: The operand '===' is representative of the FOperation FEqual, which is defined as follows: P Q P === Q Fl Fl Fl Fl Fr Ta Fl Ta Ta Fr Fl Ta Fr Fr Fr Fr Ta Ta Ta Fl Ta Ta Fr Ta Ta Ta Fr It (===) is used to show whether P and Q are identical, and whether one of them is axiomatic. FAxiom 29.4.5: The operand '(+)' is representative of the FOperation FXor, which is defined as follows: P Q P === Q Fl Fl Ta Fl Fr Fr Fl Ta Fl Fr Fl Fr Fr Fr Ta Fr Ta Fr Ta Fl Fl Ta Fr Fr Ta Ta Ta It ((+)) is used to show whether P and Q are different, and whether one of them is Frue. **** Fantasy Rule 29:5 Vanyel, Mon Dec 12 19:30:48 1994 VALID, -1 Point ==== FAxiom 29.5.1: P and Q are FVariables. **** Fantasy Rule 29:6 Stephen Turner, Mon Dec 12 20:18:49 1994 VALID, 1.5 Points ==== FAxiom 29.6.1: There are two FOperations called FLeft and FRight, that can operate on any finite number of FValues. They are denoted FL(FV0, FV1, ...) and FR(FV0, FV1, ...) where FV1, FV2, ... are the FValues the FOperations are operating upon. The FResult of these FOperations is determined as follows. The number of Frue's in the argument list minus the number of Talse's plus the sum of the positions of all the Floyd's (starting with the initial argument being reckoned as at postion 0) is calculated, and if the result is congruent to 1 modulo 3 then the FRight Foperation has Fvalue Talse, and FLeft has Fvalue Floyd; if the result is congruent to 2 modulo 3, FRight takes the Fvalue Floyd, and FLeft takes Frue; and if the result is congruent to 0 modulo 3, FRight has FValue Frue, and FLeft has the FValue Talse. For example, FR(Fr) has FValue Ta FR(Ta) has FValue Fl and FR(Fl) has FValue Fr; FL(Fr) has FValue Fl FL(Ta) has FValue Fr and FL(Fl) has FValue Ta. FAxiom 29.6.2: All FStatements in valid fantasy rules are considered to be true for the purpose of playing the fantasy rules game, whatever their FValue. FAxiom 29.6.3: All future valid fantasy rules will give the FValue of some FStatement in an earlier valid fantasy rule: furthermore, the FStatement must be one for which the FValue could not be deduced from previous information. If, however, a fantasy rule's being declared valid would mean that there was some player who had no such FStatements available to eim if e were to try and construct the next fantasy rule, that fantasy rule shall be declared invalid. FMethod 29.6.4: FMethod 29.1.1 has the FValue Frue. **** Fantasy Rule 29:7 Joshua Howard, Mon Dec 12 22:10:24 1994 INVALID, 0 Points ==== FMethod 29.1.2: All undefined FStatments have an FValue of Null (N). **** Fantasy Rule 29:8 Vanyel, Tue Dec 13 01:10:53 1994 VALID, 0 Points ==== FAxiom 29.8.1: All FValues may be abbreviated by using the first two letters of that FValue. For example, "Frue" may be abbreviated "Fr". No two FValues have the same first two letters. FAxiom 29.8.2: The FOperand '===' represents the FOperation FEqual, and is defined as follows: P === Q is Fl iff P is Floyd and Q is Floyd. Otherwise, if P and Q have the same FValue, P === Q is Frue. If P and Q do not have the same FValue, P === Q is Talse. e.g. if P is Frue and Q is Floyd, P === Q is Talse. If P is Talse and Q is Talse, P === Q is Frue. FAxiom 29.8.3: The FOperand '(+)' represents the FOperation FXor, and is defined as follows: P (+) Q is Talse if P and Q have the same FValue. If one of P or Q is Frue and the other is not, P (+) Q is Frue. If P and Q are not the same, and neither is Frue, then P (+) Q is Floyd. e.g. if P is Frue and Q is Floyd, P (+) Q is Frue. If P and Q are both Talse, P (+) Q is Talse also. FMethod 29.8.1: FMethod 29.3.1 is Frue. **** Fantasy Rule 29:9 Ronald Kunne, Wed Dec 14 13:15:08 1994 INVALID, 1 Point ==== FTheorem 29.9.1: There are exactly three FValues. FProof: From previous FStatements we know that there are at least three FValues. Assume that there are more than three. The FAxiom 29.8.2 and 29.8.3 would have given incomplete definitions for the FEqual and FXor Foperations. These FAxioms would therefore have been inconsistent and Rule 29:8 Invalid. However, Judge Oerjan judged Rule 29:8 Valid: contradiction. FAxiom 29.9.1: All future valid fantasy rules shall contain an FTheorem and its FProof. FMethod 29.9.1: The FValue of all FMethods given in valid Fantasy Rules are Frue. **** Fantasy Rule 29:10 Stein Kulseth, Wed Dec 14 13:57:52 1994 VALID, 2 Points ==== FMethod 29.9.1 If an FStatement ends with the same three words as another FStatement, then either both are Floyd, or one has the FValue Talse and the other has the FValue Frue. FAxiom 29.9.1 FTheorems consists of a series of dots (.), dashes (-), x-es (x), and/or bars (|) enclosed in angle brackets (<>). Each symbol within the brackets is considered a word. FAxiom 29.9.2 FTheorems must be deduceable from FAxioms and/or FLemmas. FAxiom 29.9.3 <.> and are FTheorems FTheorem 29.9.1 <.> FTheorem 29.9.2 FMethod 29.9.2 FTheorem 29.9.1 is Frue and FTheorem 29.9.2 is Talse **** Fantasy Rule 29:11 Jeremy D. Selengut, Wed Dec 14 19:38:54 1994 INVALID, 0 Points ==== FAxiom 29.10.1 All FStatements in valid fantasy rules have associated FLabels FAxiom 29.10.2 No two FStatements have the same FLabel FTitle 29.10.1 FAxiom 29.10.2 is known as the FLabel Exclusion Principle FAxiom 29.10.3 FLabels consist of an uninterrupted string of four digits preceded by one square left- hand bracket and followed by one square right-hand bracket FAxiom 29.10.4 The first two digits of all FLabels represent the identity of the valid fantasy rule in which the FStatement is included. The fist digit represents the tens, the second digit, the units. Valid fantasy rule are numbered in sequence with no numbers skipped FAxiom 29.10.5 The third digit of all FLabels represents the type of FStatement with which the FLabel is associated FAxiom 29.10.6 The final digit of all FLabels resolves ambiguity among multiple FStatements of the same type within the same fantasy rule. The first FStatement of a type will be assigned the digit '0' and following ones will be assigned digits in sequence FExample 29.10.1 The FLabel associated with the second FAxiom in the ninth valid fantasy rule would be [0901] FTheorem 29.10.1 There cannot be more than 10 FStatements of the same type in a single fantasy rule FProof 29.10.1 Hypothesize that there exists eleven FAxioms in the Nth valid fantasy rule. The first ten such FStatements will have the FLabels (in sequence): [nn00],[nn01],...,[nn08],[nn09] Since there are only ten digits there is no possible unique FLabel for the eleventh FAxiom. By FAxioms 29.10.1 and 2, therefore, an eleventh FStatement of a single type within one fantasy rule is impossible FMethod 29.10.1 The FValue of FTheorem 29.9.1 is Talse **** Fantasy Rule 29:12 Stein Kulseth, Thu Dec 15 15:48:07 1994 VALID, 1.5 Points ==== FAxiom 29.12.1 Iff P is the FValue of an FTheorem and Q is also the FValue of an FTheorem, and P === Q is Frue, then the symbolstring of the P-FValued Ftheorem may be concatenated by a dash (-) to the symbol- string of the Q-FValued FTheorem to form a new FTheorem. FAxiom 29.12.2 Iff P is the FValue of an FTheorem and Q is also the FValue of an FTheorem, and P (+) Q is Frue, then the symbolstring of the P-FValued Ftheorem may be concatenated by a bar (|) to the symbol- string of the Q-FValued FTheorem to form a new FTheorem. FTheorem 29.12.1 <.-.> FTheorem 29.12.2 <.|x> FMethod 29.12.1 FMethod 29.8.1 has the FValue Talse **** Fantasy Rule 29:13 Ronald Kunne, Thu Dec 15 18:46:34 1994 INVALID, 0 Points ==== FAxiom 29.10.1 : Let ? be any symbol or string of symbols. If is Frue, then <.?.> is Frue, but is Talse. FTheorem 29.10.1: <...> is Frue. FProof: Apply FAxiom 29.10.1 on FTtheorem 29.9.1 (from Stein's Rule) FAxiom 29.10.1: All future valid fantasy rules shall contain an FTheorem and its FProof. FMethod 29.10.1: The FValue of all FMethods given in Fantasy Rules with a number greater than or equal to 4 are Frue. ****