private Decomposition DecomposeWFF(Biconditional f) { List <WFF> left = new List <WFF>(); List <WFF> right = new List <WFF>(); left.Add(f.left); left.Add(f.right); right.Add(f.left.GetNegation()); right.Add(f.right.GetNegation()); return(new Decomposition(f, left, right)); }
private List <WFF> IdentityDecompose(Identity i, Biconditional f) { List <WFF> left = IdentityDecompose(i, f.left); List <WFF> right = IdentityDecompose(i, f.right); List <WFF> result = new List <WFF>(); foreach (WFF a in left) { foreach (WFF b in right) { result.Add(new Biconditional(a, b)); } } return(result); }
internal static void AddTree(this Subproof p, Tree t) { if (t == null) { throw new ArgumentNullException(); } if (t.State != TreeState.Closed) { throw new InvalidOperationException(); } if (t.decomposed == null) { // Something got a contradiction here, find out what List <WFF> all = t.getAllSentences(); WFF c1 = null; WFF c2 = null; for (int a = 0; a < all.Count; a++) { if (all[a] is Negation) { Negation n = (Negation)all[a]; if (n.inner is Identity) { Identity i = (Identity)n.inner; if (i.left.Equals(i.right)) { c1 = all[a]; break; } } } else if (all[a] is Contradiction) { c1 = all[a]; break; } bool found = false; for (int b = a + 1; b < all.Count; b++) { if (all[a].Equals(all[b].GetNegation()) || all[b].Equals(all[a].GetNegation())) { c1 = all[a]; c2 = all[b]; found = true; break; } } if (found) { break; } } Proof p1 = p.Find(c1); if (p1 == null) { throw new InvalidOperationException("p1"); } if (c2 == null) { p.steps.Add(new ProofLine(new Contradiction(), Rule.ContradictionIntro, p1)); } else { Proof p2 = p.Find(c2); if (p2 == null) { throw new InvalidOperationException("p2"); } p.steps.Add(new ProofLine(new Contradiction(), Rule.ContradictionIntro, p1, p2)); } return; } Proof d = p.Find(t.decomposed); if (t.decomposed is Biconditional) { // Add the steps for Equiv Biconditional b = (Biconditional)t.decomposed; Disjunction equ = new Disjunction( new Conjunction(b.left, b.right), new Conjunction(b.left.GetNegation(), b.right.GetNegation())); ProofLine equp = new ProofLine(equ, Rule.Equivalence, d); p.steps.Add(equp); ProofLine plleft = new ProofLine(equ.disjuncts[0], Rule.Assumption); Subproof left = new Subproof(); left.parent = p; left.assumptions.Add(plleft); left.steps.Add(new ProofLine(b.left, Rule.AndElim, plleft)); left.steps.Add(new ProofLine(b.right, Rule.AndElim, plleft)); AddTree(left, t.children[0]); p.steps.Add(left); ProofLine plright = new ProofLine(equ.disjuncts[1], Rule.Assumption); Subproof right = new Subproof(); right.parent = p; right.assumptions.Add(plright); right.steps.Add(new ProofLine(b.left.GetNegation(), Rule.AndElim, plright)); right.steps.Add(new ProofLine(b.right.GetNegation(), Rule.AndElim, plright)); AddTree(right, t.children[1]); p.steps.Add(right); p.steps.Add(new ProofLine(new Contradiction(), Rule.OrElim, equp, left, right)); } else if (t.decomposed is Conditional) { // Add the steps for Impl Conditional c = (Conditional)t.decomposed; Disjunction imp = new Disjunction(c.antecedent.GetNegation(), c.consequent); ProofLine impp = new ProofLine(imp, Rule.Implication, d); p.steps.Add(impp); Proof[] steps = new Proof[t.children.Length + 1]; steps[0] = impp; for (int a = 0; a < t.children.Length; a++) { steps[a + 1] = new Subproof(); Subproof s = (Subproof)steps[a + 1]; s.parent = p; s.assumptions.Add(new ProofLine(t.children[a].sentences[0], Rule.Assumption)); AddTree(s, t.children[a]); p.steps.Add(s); } p.steps.Add(new ProofLine(new Contradiction(), Rule.OrElim, steps)); } else if (t.decomposed is Conjunction) { foreach (WFF f in t.children[0].sentences) { p.steps.Add(new ProofLine(f, Rule.AndElim, d)); } AddTree(p, t.children[0]); } else if (t.decomposed is Disjunction) { Proof[] steps = new Proof[t.children.Length + 1]; steps[0] = d; for (int a = 0; a < t.children.Length; a++) { steps[a + 1] = new Subproof(); Subproof s = (Subproof)steps[a + 1]; s.parent = p; s.assumptions.Add(new ProofLine(t.children[a].sentences[0], Rule.Assumption)); AddTree(s, t.children[a]); p.steps.Add(s); } p.steps.Add(new ProofLine(new Contradiction(), Rule.OrElim, steps)); } else if (t.decomposed is Existential) { Subproof sub = new Subproof(); sub.parent = p; sub.assumptions.Add(new ProofLine(t.children[0].sentences[0], Rule.Assumption)); AddTree(sub, t.children[0]); p.steps.Add(sub); p.steps.Add(new ProofLine(new Contradiction(), Rule.ExistentialElim, d, sub)); } else if (t.decomposed is Identity) { // Need to add some way to find the other source foreach (WFF f in t.children[0].sentences) { p.steps.Add(new ProofLine(f, Rule.EqualsElim, d)); } AddTree(p, t.children[0]); } else if (t.decomposed is Negation) { Negation n = (Negation)t.decomposed; if (n.inner is Biconditional) { // I really hope there is a better way for this one // Add the steps for DeM and Equiv Biconditional b = (Biconditional)n.inner; ProofLine equ = new ProofLine(new Negation(new Conjunction(new Disjunction(b.left.GetNegation(), b.right), new Disjunction(b.left, b.right.GetNegation()))), Rule.Equivalence, d); p.steps.Add(equ); ProofLine dem = new ProofLine(new Disjunction(new Negation(new Disjunction(b.left.GetNegation(), b.right)), new Negation(new Disjunction(b.left, b.right.GetNegation()))), Rule.DeMorgans, equ); p.steps.Add(dem); Subproof left = new Subproof(); left.parent = p; ProofLine plleft = new ProofLine(new Negation(new Disjunction(b.left.GetNegation(), b.right)), Rule.Assumption); left.assumptions.Add(plleft); ProofLine demleft = new ProofLine(new Conjunction(b.left, b.right.GetNegation()), Rule.DeMorgans, plleft); left.steps.Add(demleft); left.steps.Add(new ProofLine(b.left, Rule.AndElim, demleft)); left.steps.Add(new ProofLine(b.right.GetNegation(), Rule.AndElim, demleft)); AddTree(left, t.children[1]); p.steps.Add(left); Subproof right = new Subproof(); right.parent = p; ProofLine plright = new ProofLine(new Negation(new Disjunction(b.left, b.right.GetNegation())), Rule.Assumption); right.assumptions.Add(plright); ProofLine demright = new ProofLine(new Conjunction(b.left.GetNegation(), b.right), Rule.DeMorgans, plright); right.steps.Add(demright); right.steps.Add(new ProofLine(b.left.GetNegation(), Rule.AndElim, demright)); right.steps.Add(new ProofLine(b.right, Rule.AndElim, demright)); AddTree(right, t.children[0]); p.steps.Add(right); p.steps.Add(new ProofLine(new Contradiction(), Rule.OrElim, dem, left, right)); } else if (n.inner is Conditional) { // Add the steps for DeM and Impl Conditional c = (Conditional)n.inner; ProofLine imp = new ProofLine(new Negation(new Disjunction(c.antecedent.GetNegation(), c.consequent)), Rule.Implication, d); p.steps.Add(imp); ProofLine dem = new ProofLine(new Conjunction(c.antecedent, c.consequent.GetNegation()), Rule.DeMorgans, imp); p.steps.Add(dem); p.steps.Add(new ProofLine(c.antecedent, Rule.AndElim, dem)); p.steps.Add(new ProofLine(c.consequent.GetNegation(), Rule.AndElim, dem)); AddTree(p, t.children[0]); } else if (n.inner is Conjunction) { // Add the steps for DeM Conjunction i = (Conjunction)n.inner; List <WFF> neg = new List <WFF>(); foreach (WFF f in i.conjuncts) { neg.Add(f.GetNegation()); } Disjunction dem = new Disjunction(neg.ToArray()); ProofLine demp = new ProofLine(dem, Rule.DeMorgans, d); p.steps.Add(demp); Proof[] steps = new Proof[t.children.Length + 1]; steps[0] = demp; for (int a = 0; a < t.children.Length; a++) { steps[a + 1] = new Subproof(); Subproof s = (Subproof)steps[a + 1]; s.parent = p; s.assumptions.Add(new ProofLine(t.children[a].sentences[0], Rule.Assumption)); AddTree(s, t.children[a]); p.steps.Add(s); } p.steps.Add(new ProofLine(new Contradiction(), Rule.OrElim, steps)); } else if (n.inner is Disjunction) { // Add the steps for DeM Disjunction i = (Disjunction)n.inner; List <WFF> neg = new List <WFF>(); foreach (WFF f in i.disjuncts) { neg.Add(f.GetNegation()); } Conjunction dem = new Conjunction(neg.ToArray()); ProofLine demp = new ProofLine(dem, Rule.DeMorgans, d); p.steps.Add(demp); foreach (WFF f in t.children[0].sentences) { p.steps.Add(new ProofLine(f, Rule.AndElim, demp)); } AddTree(p, t.children[0]); } else if (n.inner is Existential) { // Add the steps for DeM p.steps.Add(new ProofLine(t.children[0].sentences[0], Rule.DeMorgans, d)); AddTree(p, t.children[0]); } else if (n.inner is Negation) { p.steps.Add(new ProofLine(t.children[0].sentences[0], Rule.NotElim, d)); AddTree(p, t.children[0]); } else if (n.inner is Universal) { // Add the steps for DeM p.steps.Add(new ProofLine(t.children[0].sentences[0], Rule.DeMorgans, d)); AddTree(p, t.children[0]); } } else if (t.decomposed is Universal) { foreach (WFF f in t.children[0].sentences) { p.steps.Add(new ProofLine(f, Rule.UniversalElim, d)); } AddTree(p, t.children[0]); } }
private Decomposition DecomposeWFF(Negation f) { if (f.inner is AtomicWFF) { return(null); } else if (f.inner is Biconditional) { Biconditional inner = (Biconditional)f.inner; List <WFF> left = new List <WFF>(); List <WFF> right = new List <WFF>(); left.Add(inner.left.GetNegation()); left.Add(inner.right); right.Add(inner.left); right.Add(inner.right.GetNegation()); return(new Decomposition(f, left, right)); } else if (f.inner is Conditional) { Conditional inner = (Conditional)f.inner; List <WFF> left = new List <WFF>(); left.Add(inner.antecedent); left.Add(inner.consequent.GetNegation()); return(new Decomposition(f, left)); } else if (f.inner is Conjunction) { Conjunction inner = (Conjunction)f.inner; List <WFF>[] conjuncts = new List <WFF> [inner.arity]; for (int a = 0; a < inner.arity; a++) { conjuncts[a] = new List <WFF>(); conjuncts[a].Add(inner.conjuncts[a].GetNegation()); } return(new Decomposition(f, conjuncts.ToArray())); } else if (f.inner is Disjunction) { Disjunction inner = (Disjunction)f.inner; List <WFF> disjuncts = new List <WFF>(); foreach (WFF d in inner.disjuncts) { disjuncts.Add(d.GetNegation()); } return(new Decomposition(f, disjuncts)); } else if (f.inner is Existential) { Existential inner = (Existential)f.inner; List <WFF> dec = new List <WFF>(); dec.Add(new Universal(inner.variable, inner.scope.GetNegation())); return(new Decomposition(f, dec)); } else if (f.inner is Negation) { Negation inner = (Negation)f.inner; List <WFF> dec = new List <WFF>(); dec.Add(inner.inner); return(new Decomposition(f, dec)); } else if (f.inner is Universal) { Universal inner = (Universal)f.inner; List <WFF> dec = new List <WFF>(); dec.Add(new Existential(inner.variable, inner.scope.GetNegation())); return(new Decomposition(f, dec)); } throw new NotImplementedException(f.inner.GetType().ToString()); }
private Node CreateABinaryTree(ref string formula, Node node) { if (node == null) { switch (formula[0]) { case '~': formula = formula.Remove(0, 1); node = new Negation(null); break; case '>': formula = formula.Remove(0, 1); node = new Implication(null, null); break; case '=': formula = formula.Remove(0, 1); node = new Biconditional(null, null); break; case '&': formula = formula.Remove(0, 1); node = new Conjunction(null, null); break; case '|': formula = formula.Remove(0, 1); node = new Disjunction(null, null); break; case '%': formula = formula.Remove(0, 1); formula = formula.Insert(0, "&"); node = new Negation(null); break; case '(': formula = formula.Remove(0, 1); return(this.CreateABinaryTree(ref formula, node)); case ',': formula = formula.Remove(0, 1); return(this.CreateABinaryTree(ref formula, node)); case ')': formula = formula.Remove(0, 1); return(this.CreateABinaryTree(ref formula, node)); default: node = new Leaf(formula[0]); if (!leaves.Exists(e => e == node.Value)) { this.leaves.Add(node.Value); } formula = formula.Remove(0, 1); break; } if (!(node is Leaf)) { node.leftChild = CreateABinaryTree(ref formula, node.leftChild); } if (!(node is Negation) && !(node is Leaf)) { node.rightChild = CreateABinaryTree(ref formula, node.rightChild); } return(node); } else { return(node); } }