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- "* Constructing TRUTH TABLES and comparing propositions *"
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- "* in a max/min MULTI-VALUED (w-valued) modal LOGIC *"
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- "* (c)Eugenio Roanes-Lozano (Dept. Algebra, Univ. Complutense Madrid) Jan 00 *"
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- "-----------------------------------------------------------------------------"
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- "w-valued modal Logic (w should be a prime number), 0=false, 1=true. "
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- "Connectives begin with an ``M'' (multivalued) not to interfere the built-in. "
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- "-----------------------------------------------------------------------------"
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- "The propositional variables: p,q,r,s,u,v"
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- p:=1/(w-1)*MOD(FLOOR(j_/w^0),w)
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- q:=1/(w-1)*MOD(FLOOR(j_/w^1),w)
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- r:=1/(w-1)*MOD(FLOOR(j_/w^2),w)
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- s:=1/(w-1)*MOD(FLOOR(j_/w^3),w)
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- u:=1/(w-1)*MOD(FLOOR(j_/w^4),w)
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- v:=1/(w-1)*MOD(FLOOR(j_/w^5),w)
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- "List of propositional variables (more could be added above):"
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- vp:=[p,q,r,s,u,v]
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- "Tautology and contradiction"
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- t:=1
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- c:=0
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- "Logic connectives: negation, possible, necessary, or, and (prefix form)"
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- MNEG(a_):=1-a_
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- MPOS(a_):=1-FLOOR(1-a_)
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- MNEC(a_):=FLOOR(a_)
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- MOR(a_,b_):=MAX(a_,b_)
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- MAND(a_,b_):=MIN(a_,b_)
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- "Truth tables: propositional variables that can be used in TT(m_,a_,b_):"
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- "the first m_ in P,Q,R,S,U,V plus tautology (T) and contradiction (C). "
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- TT(m_,a_,b_):=VECTOR(APPEND(VECTOR(vp SUB i_,i_,1,m_),[a_,b_]),j_,0,w^m_-1)
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- "-----------------------------------------------------------------------------"
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- "Conditional and biconditional (Kleene-style)"
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- MIMP(a_,b_):=MOR(MNEG(a_),b_)
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- MIFF(a_,b_):=MAND(MIMP(a_,b_),MIMP(b_,a_))
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- "-----------------------------------------------------------------------------"
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- "Is it a tautology? (i.e.: Is it always true?). Answers: 1->yes, 0->no"
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- ISTAUT(m_,a_):=IF(PRODUCT(a_,j_,0,w^m_-1)=1,1,0)
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- "-----------------------------------------------------------------------------"
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- "Is ``b'' a tautological consequence of ``a''? (i.e.: Is the consequent true"
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- "whenever the antecedent is true?). Answers: 1->yes, 0->no"
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- ISCONSTAUT(m_,a_,b_):=IF(PRODUCT(IF(a_=1,b_,1),j_,0,w^m_-1)=1,1,0)
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- "--------------------------- END OF .MTH FILE ---------------------------"