diff --git a/src/ltlast/atomic_prop.cc b/src/ltlast/atomic_prop.cc
index 536a14c14..df9962855 100644
--- a/src/ltlast/atomic_prop.cc
+++ b/src/ltlast/atomic_prop.cc
@@ -45,6 +45,11 @@ namespace spot
       is.sere_formula = true;
       is.eventual = false;
       is.universal = false;
+      is.syntactic_safety = true;
+      is.syntactic_guarantee = true;
+      is.syntactic_obligation = true;
+      is.syntactic_recurrence = true;
+      is.syntactic_persistence = true;
       is.not_marked = true;
       is.accepting_eword = false;
     }
diff --git a/src/ltlast/automatop.cc b/src/ltlast/automatop.cc
index 303842f40..826e97480 100644
--- a/src/ltlast/automatop.cc
+++ b/src/ltlast/automatop.cc
@@ -41,6 +41,11 @@ namespace spot
       is.sere_formula = false;
       is.eventual = false;
       is.universal = false;
+      is.syntactic_safety = false;
+      is.syntactic_guarantee = false;
+      is.syntactic_obligation = false;
+      is.syntactic_recurrence = false;
+      is.syntactic_persistence = false;
       is.not_marked = true;
       is.accepting_eword = false;
 
diff --git a/src/ltlast/binop.cc b/src/ltlast/binop.cc
index bc9cf56e8..765652084 100644
--- a/src/ltlast/binop.cc
+++ b/src/ltlast/binop.cc
@@ -53,17 +53,69 @@ namespace spot
       switch (op)
 	{
 	case Xor:
-	case Implies:
 	case Equiv:
 	  is.sere_formula = is.boolean;
 	  is.sugar_free_boolean = false;
 	  is.in_nenoform = false;
+	  // is.syntactic_obligation inherited;
+	  is.accepting_eword = false;
+	  if (is.syntactic_obligation)
+	    {
+	      // Only formula that are in the intersection of
+	      // guarantee and safety are closed by Xor and <=>.
+	      bool sg = is.syntactic_safety && is.syntactic_guarantee;
+	      bool rp = is.syntactic_recurrence && is.syntactic_persistence;
+	      is.syntactic_safety = sg;
+	      is.syntactic_guarantee = sg;
+	      is.syntactic_recurrence = rp;
+	      is.syntactic_persistence = rp;
+	    }
+	  else
+	    {
+	      is.syntactic_safety = false;
+	      is.syntactic_guarantee = false;
+	    }
+	  break;
+	case Implies:
+	  is.sere_formula = is.boolean;
+	  is.sugar_free_boolean = false;
+	  is.in_nenoform = false;
+	  is.syntactic_safety =
+	    first->is_syntactic_obligation() && second->is_syntactic_safety();
+	  is.syntactic_obligation =
+	    first->is_syntactic_safety() && second->is_syntactic_obligation();
+	  // is.syntactic_obligation inherited
+	  is.syntactic_persistence = first->is_syntactic_recurrence()
+	    && second->is_syntactic_persistence();
+	  is.syntactic_recurrence = first->is_syntactic_persistence()
+	    && second->is_syntactic_recurrence();
 	  is.accepting_eword = false;
 	  break;
 	case EConcatMarked:
 	  is.not_marked = false;
 	  // fall through
 	case EConcat:
+	  is.ltl_formula = false;
+	  is.boolean = false;
+	  is.eltl_formula = false;
+	  is.sere_formula = false;
+	  is.accepting_eword = false;
+	  is.psl_formula = true;
+
+	  // FIXME: if we know that the SERE has a finite language.
+	  // (i.e. no star).  Then
+	  // is.syntactic_safety = second->is_syntactic_safety();
+	  // is.syntactic_obligation = second->is_syntactic_obligation();
+	  // is.syntactic_recurrence = second->is_syntactic_recurrence();
+	  is.syntactic_safety = false;
+	  is.syntactic_guarantee = second->is_syntactic_guarantee();
+	  is.syntactic_obligation = second->is_syntactic_guarantee();
+	  is.syntactic_recurrence = second->is_syntactic_guarantee();
+	  is.syntactic_persistence = second->is_syntactic_persistence();
+
+	  assert(first->is_sere_formula());
+	  assert(second->is_psl_formula());
+	  break;
 	case UConcat:
 	  is.ltl_formula = false;
 	  is.boolean = false;
@@ -71,6 +123,18 @@ namespace spot
 	  is.sere_formula = false;
 	  is.accepting_eword = false;
 	  is.psl_formula = true;
+
+	  // FIXME: if we know that the SERE has a finite language.
+	  // (i.e. no star).  Then
+	  // is.syntactic_guarantee = second->is_syntactic_guarantee();
+	  // is.syntactic_obligation = second->is_syntactic_obligation();
+	  // is.syntactic_persistence = second->is_syntactic_persistence();
+	  is.syntactic_safety = second->is_syntactic_safety();
+	  is.syntactic_guarantee = false;
+	  is.syntactic_obligation = second->is_syntactic_safety();
+	  is.syntactic_recurrence = second->is_syntactic_recurrence();
+	  is.syntactic_persistence = second->is_syntactic_safety();
+
 	  assert(first->is_sere_formula());
 	  assert(second->is_psl_formula());
 	  break;
@@ -82,6 +146,16 @@ namespace spot
 	  is.eltl_formula = false;
 	  is.sere_formula = false;
 	  is.accepting_eword = false;
+
+	  is.syntactic_safety = false;
+	  // is.syntactic_guarantee = Guarantee U Guarantee
+	  is.syntactic_obligation = // Obligation U Guarantee
+	    first->is_syntactic_obligation()
+	    && second->is_syntactic_guarantee();
+	  is.syntactic_recurrence = // Recurrence U Guarantee
+	    first->is_syntactic_recurrence()
+	    && second->is_syntactic_guarantee();
+	  // is.syntactic_persistence = Persistence U Persistance
 	  break;
 	case W:
 	  // a W 0 = Ga
@@ -91,6 +165,16 @@ namespace spot
 	  is.eltl_formula = false;
 	  is.sere_formula = false;
 	  is.accepting_eword = false;
+
+	  // is.syntactic_safety = Safety W Safety;
+	  is.syntactic_guarantee = false;
+	  is.syntactic_obligation = // Safety W Obligation
+	    first->is_syntactic_safety() && second->is_syntactic_obligation();
+	  // is.syntactic_recurrence = Recurrence W Recurrence
+	  is.syntactic_persistence = // Safety W Persistance
+	    first->is_syntactic_safety()
+	    && second->is_syntactic_persistence();
+
 	  break;
 	case R:
 	  // 0 R a = Ga
@@ -100,6 +184,16 @@ namespace spot
 	  is.eltl_formula = false;
 	  is.sere_formula = false;
 	  is.accepting_eword = false;
+
+	  // is.syntactic_safety = Safety R Safety;
+	  is.syntactic_guarantee = false;
+	  is.syntactic_obligation = // Obligation R Safety
+	    first->is_syntactic_obligation() && second->is_syntactic_safety();
+	  //is.syntactic_recurrence = Recurrence R Recurrence
+	  is.syntactic_persistence = // Persistence R Safety
+	    first->is_syntactic_persistence()
+	    && second->is_syntactic_safety();
+
 	  break;
 	case M:
 	  // a M 1 = Fa
@@ -109,8 +203,22 @@ namespace spot
 	  is.eltl_formula = false;
 	  is.sere_formula = false;
 	  is.accepting_eword = false;
+
+	  is.syntactic_safety = false;
+	  // is.syntactic_guarantee = Guarantee M Guarantee
+	  is.syntactic_obligation = // Guarantee M Obligation
+	    first->is_syntactic_guarantee()
+	    && second->is_syntactic_obligation();
+	  is.syntactic_recurrence = // Guarantee M Recurrence
+	    first->is_syntactic_guarantee()
+	    && second->is_syntactic_recurrence();
+	  // is.syntactic_persistence = Persistence M Persistance
+
 	  break;
 	}
+
+      assert((!is.syntactic_obligation) ||
+	     (is.syntactic_persistence && is.syntactic_recurrence));
     }
 
     binop::~binop()
diff --git a/src/ltlast/bunop.cc b/src/ltlast/bunop.cc
index 487a5f737..e59e18d81 100644
--- a/src/ltlast/bunop.cc
+++ b/src/ltlast/bunop.cc
@@ -42,6 +42,11 @@ namespace spot
       is.psl_formula = false;
       is.eventual = false;
       is.universal = false;
+      is.syntactic_safety = false;
+      is.syntactic_guarantee = false;
+      is.syntactic_obligation = false;
+      is.syntactic_recurrence = false;
+      is.syntactic_persistence = false;
 
       switch (op_)
 	{
diff --git a/src/ltlast/constant.cc b/src/ltlast/constant.cc
index b98daa377..60bcb70e4 100644
--- a/src/ltlast/constant.cc
+++ b/src/ltlast/constant.cc
@@ -51,6 +51,11 @@ namespace spot
 	  is.sere_formula = true;
 	  is.eventual = true;
 	  is.universal = true;
+	  is.syntactic_safety = true;
+	  is.syntactic_guarantee = true;
+	  is.syntactic_obligation = true;
+	  is.syntactic_recurrence = true;
+	  is.syntactic_persistence = true;
 	  is.not_marked = true;
 	  is.accepting_eword = false;
 	  break;
@@ -65,6 +70,11 @@ namespace spot
 	  is.psl_formula = false;
 	  is.sere_formula = true;
 	  is.eventual = false;
+	  is.syntactic_safety = false;
+	  is.syntactic_guarantee = false;
+	  is.syntactic_obligation = false;
+	  is.syntactic_recurrence = false;
+	  is.syntactic_persistence = false;
 	  is.universal = false;
 	  is.not_marked = true;
 	  is.accepting_eword = true;
diff --git a/src/ltlast/formula.cc b/src/ltlast/formula.cc
index 494db40c6..d2624a072 100644
--- a/src/ltlast/formula.cc
+++ b/src/ltlast/formula.cc
@@ -86,6 +86,11 @@ namespace spot
       proprint(is_sere_formula, "S", "SERE formula");
       proprint(is_eventual, "e", "pure eventuality");
       proprint(is_universal, "u", "purely universal");
+      proprint(is_syntactic_safety, "s", "syntactic safety");
+      proprint(is_syntactic_guarantee, "g", "syntactic guarantee");
+      proprint(is_syntactic_obligation, "o", "syntactic obligation");
+      proprint(is_syntactic_persistence, "p", "syntactic persistence");
+      proprint(is_syntactic_recurrence, "r", "syntactic recurrence");
       proprint(is_marked, "+", "marked");
       proprint(accepts_eword, "0", "accepts the empty word");
       return out;
diff --git a/src/ltlast/formula.hh b/src/ltlast/formula.hh
index 681deb443..f9d32bb88 100644
--- a/src/ltlast/formula.hh
+++ b/src/ltlast/formula.hh
@@ -226,6 +226,36 @@ namespace spot
 	return is.universal;
       }
 
+      /// Whether a PSL/LTL formula is syntactic safety property.
+      bool is_syntactic_safety() const
+      {
+	return is.syntactic_safety;
+      }
+
+      /// Whether a PSL/LTL formula is syntactic guarantee property.
+      bool is_syntactic_guarantee() const
+      {
+	return is.syntactic_guarantee;
+      }
+
+      /// Whether a PSL/LTL formula is syntactic obligation property.
+      bool is_syntactic_obligation() const
+      {
+	return is.syntactic_obligation;
+      }
+
+      /// Whether a PSL/LTL formula is syntactic recurrence property.
+      bool is_syntactic_recurrence() const
+      {
+	return is.syntactic_recurrence;
+      }
+
+      /// Whether a PSL/LTL formula is syntactic persistence property.
+      bool is_syntactic_persistence() const
+      {
+	return is.syntactic_persistence;
+      }
+
       /// Whether the formula has an occurrence of EConcatMarked.
       bool is_marked() const
       {
@@ -288,6 +318,11 @@ namespace spot
 	bool sere_formula:1;	   // Only SERE operators.
 	bool eventual:1;	   // Purely eventual formula.
 	bool universal:1;	   // Purely universal formula.
+	bool syntactic_safety:1;   // Syntactic Safety Property.
+	bool syntactic_guarantee:1;   // Syntactic Guarantee Property.
+	bool syntactic_obligation:1;  // Syntactic Obligation Property.
+	bool syntactic_recurrence:1;  // Syntactic Recurrence Property.
+	bool syntactic_persistence:1; // Syntactic Persistence Property.
 	bool not_marked:1;	   // No occurrence of EConcatMarked.
 	bool accepting_eword:1;	   // Accepts the empty word.
       };
diff --git a/src/ltlast/unop.cc b/src/ltlast/unop.cc
index df3661768..72df7b3d0 100644
--- a/src/ltlast/unop.cc
+++ b/src/ltlast/unop.cc
@@ -41,6 +41,13 @@ namespace spot
 	case Not:
 	  is.in_nenoform = (child->kind() == AtomicProp);
 	  is.sere_formula = is.boolean;
+
+	  is.syntactic_safety = child->is_syntactic_guarantee();
+	  is.syntactic_guarantee = child->is_syntactic_safety();
+	  // is.syntactic_obligation inherited from child
+	  is.syntactic_recurrence = child->is_syntactic_persistence();
+	  is.syntactic_persistence = child->is_syntactic_recurrence();
+
 	  is.accepting_eword = false;
 	  break;
 	case X:
@@ -48,6 +55,11 @@ namespace spot
 	  is.X_free = false;
 	  is.eltl_formula = false;
 	  is.sere_formula = false;
+	  // is.syntactic_safety inherited
+	  // is.syntactic_guarantee inherited
+	  // is.syntactic_obligation inherited
+	  // is.syntactic_recurrence inherited
+	  // is.syntactic_persistence inherited
 	  is.accepting_eword = false;
 	  break;
 	case F:
@@ -56,6 +68,11 @@ namespace spot
 	  is.sere_formula = false;
 	  is.sugar_free_ltl = false;
 	  is.eventual = true;
+	  is.syntactic_safety = false;
+	  // is.syntactic_guarantee inherited
+	  is.syntactic_obligation = is.syntactic_guarantee;
+	  is.syntactic_recurrence = is.syntactic_guarantee;
+	  // is.syntactic_persistence inherited
 	  is.accepting_eword = false;
 	  break;
 	case G:
@@ -64,6 +81,11 @@ namespace spot
 	  is.sere_formula = false;
 	  is.sugar_free_ltl = false;
 	  is.universal = true;
+	  // is.syntactic_safety inherited
+	  is.syntactic_guarantee = false;
+	  is.syntactic_obligation = is.syntactic_safety;
+	  // is.syntactic_recurrence inherited
+	  is.syntactic_persistence = is.syntactic_safety;
 	  is.accepting_eword = false;
 	  break;
 	case Finish:
@@ -71,17 +93,38 @@ namespace spot
 	  is.ltl_formula = false;
 	  is.psl_formula = false;
 	  is.sere_formula = false;
+	  is.syntactic_safety = false;
+	  is.syntactic_guarantee = false;
+	  is.syntactic_obligation = false;
+	  is.syntactic_recurrence = false;
+	  is.syntactic_persistence = false;
 	  is.accepting_eword = false;
 	  break;
 	case NegClosure:
 	  is.not_marked = false;
-	  // fall through
+	  is.boolean = false;
+	  is.ltl_formula = false;
+	  is.eltl_formula = false;
+	  is.psl_formula = true;
+	  is.sere_formula = false;
+	  is.syntactic_safety = true;
+	  is.syntactic_guarantee = true;
+	  is.syntactic_obligation = true;
+	  is.syntactic_recurrence = true;
+	  is.syntactic_persistence = true;
+	  is.accepting_eword = false;
+	  break;
 	case Closure:
 	  is.boolean = false;
 	  is.ltl_formula = false;
 	  is.eltl_formula = false;
 	  is.psl_formula = true;
 	  is.sere_formula = false;
+	  is.syntactic_safety = true;
+	  is.syntactic_guarantee = true;
+	  is.syntactic_obligation = true;
+	  is.syntactic_recurrence = true;
+	  is.syntactic_persistence = true;
 	  is.accepting_eword = false;
 	  assert(child->is_sere_formula());
 	  break;
diff --git a/src/ltltest/kind.test b/src/ltltest/kind.test
index 85954c96d..ec4f79886 100755
--- a/src/ltltest/kind.test
+++ b/src/ltltest/kind.test
@@ -33,28 +33,61 @@ check()
     test "$word" = "$2"
 }
 
-check 'a'         'B&!xfLEPS'
-check 'a<->b'     'BxfLEPS'
-check '!a'        'B&!xfLEPS'
-check '!(a|b)'    'B&xfLEPS'
-check 'F(a)'      '&!xLPe'
-check 'G(a)'      '&!xLPu'
-check 'a U b'     '&!xfLP'
-check 'a U Fb'    '&!xLP'
-check 'Ga U b'    '&!xLP'
-check '1 U a'     '&!xfLPe'
-check 'a W b'     '&!xfLP'
-check 'a W 0'     '&!xfLPu'
-check 'a M b'     '&!xfLP'
-check 'a M 1'     '&!xfLPe'
-check 'a R b'     '&!xfLP'
-check '0 R b'     '&!xfLPu'
-check '{a;b}|->!Xb' '&fP'
-check '{a;b}|->X!b' '&!fP'
-check '{a;b}|->!Gb' '&xP'
-check '{a;b}|->F!b' '&!xP'
-check '{a:b:c:d}!' 'B&!xfLEPS'  # Equivalent to a&b&c&d
-check 'a&b&c&d'    'B&!xfLEPS'
+check 'a'         'B&!xfLEPSsgopr'
+check 'a<->b'     'BxfLEPSsgopr'
+check '!a'        'B&!xfLEPSsgopr'
+check '!(a|b)'    'B&xfLEPSsgopr'
+check 'F(a)'      '&!xLPegopr'
+check 'G(a)'      '&!xLPusopr'
+check 'a U b'     '&!xfLPgopr'
+check 'a U Fb'    '&!xLPgopr'
+check 'Ga U b'    '&!xLPopr'
+check '1 U a'     '&!xfLPegopr'
+check 'a W b'     '&!xfLPsopr'
+check 'a W 0'     '&!xfLPusopr'
+check 'a M b'     '&!xfLPgopr'
+check 'a M 1'     '&!xfLPegopr'
+check 'a R b'     '&!xfLPsopr'
+check '0 R b'     '&!xfLPusopr'
+check 'a R (b R (c R d))' '&!xfLPsopr'
+check 'a U (b U (c U d))' '&!xfLPgopr'
+check 'a W (b W (c W d))' '&!xfLPsopr'
+check 'a M (b M (c M d))' '&!xfLPgopr'
+check '{a;c*;b}|->!Xb' '&fPsopr'
+check '{a;c*;b}|->X!b' '&!fPsopr'
+check '{a;c*;b}|->!Fb' '&xPsopr'
+check '{a;c*;b}|->G!b' '&!xPsopr'
+check '{a;c*;b}|->!Gb' '&xPr'
+check '{a;c*;b}|->F!b' '&!xPr'
+check '{a;c*;b}|->GFa' '&!xPr'
+check '{a;c*;b}|->FGa' '&!xP'
+check '{a;c*;b}<>->!Gb' '&xPgopr'
+check '{a;c*;b}<>->F!b' '&!xPgopr'
+check '{a;c*;b}<>->FGb' '&!xPp'
+check '{a;c*;b}<>->!GFb' '&xPp'
+check '{a:b:c:d}!' 'B&!xfLEPSsgopr'  # Equivalent to a&b&c&d
+check 'a&b&c&d'    'B&!xfLEPSsgopr'
+check '(Xa <-> XXXc) U (b & Fe)' 'LPgopr'
+check '(!X(a|X(!b))&(FX(g xor h)))U(!G(a|b))' 'LPgopr'
+check '(!X(a|X(!b))&(GX(g xor h)))R(!F(a|b))' 'LPsopr'
+check '(!X(a|X(!b))&(GX(g xor h)))U(!G(a|b))' 'LPopr'
+check '(!X(a|X(!b))&(FX(g xor h)))R(!F(a|b))' 'LPopr'
+check '(!X(a|X(!b))&(GX(g xor h)))U(!F(a|b))' 'LPp'
+check '(!X(a|X(!b))&(FX(g xor h)))R(!G(a|b))' 'LPr'
+check '(!X(a|GXF(!b))&(FGX(g xor h)))U(!F(a|b))' 'LPp'
+check '(!X(a|GXF(!b))&(FGX(g xor h)))R(!F(a|b))' 'LPp'
+check '(!X(a|FXG(!b))&(GFX(g xor h)))R(!G(a|b))' 'LPr'
+check '(!X(a|FXG(!b))&(GFX(g xor h)))U(!G(a|b))' 'LPr'
+check '(!X(a|GXF(!b))&(FGX(g xor h)))U(!G(a|Fb))' 'LPp'
+check '(!X(a|GXF(!b))&(FGX(g xor h)))U(!F(a|Gb))' 'LP'
+check '(!X(a|FXG(!b))&(GFX(g xor h)))R(!F(a|Gb))' 'LPr'
+check '(!X(a|FXG(!b))&(GFX(g xor h)))R(!G(a|Fb))' 'LP'
+check 'GFa M GFb' '&!xLPeu'
+check 'FGa M FGb' '&!xLPeup'
+check 'Fa  M GFb' '&!xLPer'
+check 'GFa W GFb' '&!xLPeur'
+check 'FGa W FGb' '&!xLPeu'
+check 'Ga  W FGb' '&!xLPup'
 
 run 0 ../consterm '1'
 run 0 ../consterm '0'