diff --git a/unit_tests/engine/test_filter_evttype_resolver.cpp b/unit_tests/engine/test_filter_evttype_resolver.cpp
index 30d7e7c2..dce6ab38 100644
--- a/unit_tests/engine/test_filter_evttype_resolver.cpp
+++ b/unit_tests/engine/test_filter_evttype_resolver.cpp
@@ -19,6 +19,8 @@ limitations under the License.
 #include <sinsp.h>
 #include <filter/parser.h>
 
+#define ASSERT_FILTER_EQ(a, b) { ASSERT_EQ(get_filter_set(a), get_filter_set(b)); }
+
 std::set<uint16_t> get_filter_set(const string &fltstr)
 {
 	set<uint16_t> actual;
@@ -72,7 +74,7 @@ TEST(EvtTypeResolver, check_openat)
 	ASSERT_EQ(get_filter_set("evt.type!=openat"), not_openat);
 	ASSERT_EQ(get_filter_set("not not not evt.type = openat"), not_openat);
 	ASSERT_EQ(get_filter_set("not evt.type=openat"), not_openat);
-	ASSERT_EQ(get_filter_set("evt.type=close or not (evt.type=openat and proc.name=nginx)"), not_openat);
+	ASSERT_EQ(get_filter_set("evt.type=close or evt.type!=openat"), not_openat);
 }
 
 TEST(EvtTypeResolver, check_openat_or_close)
@@ -106,6 +108,8 @@ TEST(EvtTypeResolver, check_all_events)
 	ASSERT_EQ(get_filter_set("evt.type=openat or proc.name=nginx"), all_events);
 	ASSERT_EQ(get_filter_set("evt.type=openat or (proc.name=nginx)"), all_events);
 	ASSERT_EQ(get_filter_set("(evt.type=openat) or proc.name=nginx"), all_events);
+	ASSERT_EQ(get_filter_set("evt.type=close or not (evt.type=openat and proc.name=nginx)"), all_events);
+	ASSERT_EQ(get_filter_set("evt.type=openat or not (evt.type=close and proc.name=nginx)"), all_events);
 }
 
 TEST(EvtTypeResolver, check_no_events)
@@ -116,3 +120,112 @@ TEST(EvtTypeResolver, check_no_events)
 	ASSERT_EQ(get_filter_set("evt.type=openat and (evt.type=close and proc.name=nginx)"), no_events);
 	ASSERT_EQ(get_filter_set("evt.type=openat and (evt.type=close)"), no_events);
 }
+
+TEST(EvtTypeResolver, check_properties)
+{
+	std::set<uint16_t> no_events = {};
+
+	// see: https://github.com/falcosecurity/libs/pull/854#issuecomment-1411151732
+	ASSERT_FILTER_EQ(
+		"evt.type in (connect, execve, accept, mmap, container) and not (proc.name=cat and evt.type=mmap)",
+		"evt.type in (accept, connect, container, execve, mmap)");
+	ASSERT_EQ(get_filter_set("(evt.type=mmap and not evt.type=mmap)"), no_events);
+
+	// defining algebraic base sets
+	std::string zerof = "(evt.type in ())"; ///< "zero"-set: no evt type should matches the filter
+	std::string onef = "(evt.type exists)"; ///< "one"-set: all evt types should match the filter
+	std::string neutral1 = "(proc.name=cat)"; ///< "neutral"-sets: evt types are not checked in the filter
+	std::string neutral2 = "(not proc.name=cat)";
+	ASSERT_FILTER_EQ(onef, neutral1);
+	ASSERT_FILTER_EQ(onef, neutral2);
+
+	// algebraic set properties
+	// 1' = 0
+	ASSERT_FILTER_EQ("not " + onef, zerof);
+	// 0' = 1
+	ASSERT_FILTER_EQ("not " + zerof, onef);
+	// (A')' = A
+	ASSERT_FILTER_EQ("evt.type=mmap", "not (not evt.type=mmap)");
+	// A * A' = 0
+	ASSERT_EQ(get_filter_set(zerof), no_events);
+	// A + A' = 1
+	ASSERT_FILTER_EQ("evt.type=mmap or not evt.type=mmap", onef);
+	ASSERT_FILTER_EQ("evt.type=mmap or not evt.type=mmap", neutral1);
+	ASSERT_FILTER_EQ("evt.type=mmap or not evt.type=mmap", neutral2);
+	// 0 * 1 = 0
+	ASSERT_FILTER_EQ(zerof + " and " + onef, zerof);
+	ASSERT_FILTER_EQ(zerof + " and " + neutral1, zerof);
+	ASSERT_FILTER_EQ(zerof + " and " + neutral2, zerof);
+	// 0 + 1 = 1
+	ASSERT_FILTER_EQ(zerof + " or " + onef, onef);
+	ASSERT_FILTER_EQ(zerof + " or " + neutral1, onef);
+	ASSERT_FILTER_EQ(zerof + " or " + neutral2, onef);
+	// A * 0 = 0
+	ASSERT_FILTER_EQ("evt.type=mmap and " + zerof, zerof);
+	// A * 1 = A
+	ASSERT_FILTER_EQ("evt.type=mmap and " + onef, "evt.type=mmap");
+	ASSERT_FILTER_EQ("evt.type=mmap and " + neutral1, "evt.type=mmap");
+	ASSERT_FILTER_EQ("evt.type=mmap and " + neutral2, "evt.type=mmap");
+	// A + 0 = A
+	ASSERT_FILTER_EQ("evt.type=mmap or " + zerof, "evt.type=mmap");
+	// A + 1 = 1
+	ASSERT_FILTER_EQ("evt.type=mmap or " + onef, onef);
+	ASSERT_FILTER_EQ("evt.type=mmap or " + neutral1, onef);
+	ASSERT_FILTER_EQ("evt.type=mmap or " + neutral2, onef);
+	// A + A = A
+	ASSERT_FILTER_EQ("evt.type=mmap or evt.type=mmap", "evt.type=mmap");
+	// A * A = A
+	ASSERT_FILTER_EQ("evt.type=mmap and evt.type=mmap", "evt.type=mmap");
+
+	// de morgan's laws
+	ASSERT_FILTER_EQ(
+		"not (proc.name=cat or evt.type=mmap)",
+		"not proc.name=cat and not evt.type=mmap");
+	ASSERT_FILTER_EQ(
+		"not (proc.name=cat or fd.type=file)",
+		"not proc.name=cat and not fd.type=file");
+	ASSERT_FILTER_EQ(
+		"not (evt.type=execve or evt.type=mmap)",
+		"not evt.type=execve and not evt.type=mmap");
+	ASSERT_FILTER_EQ(
+		"not (evt.type=mmap or evt.type=mmap)",
+		"not evt.type=mmap and not evt.type=mmap");
+	ASSERT_FILTER_EQ(
+		"not (proc.name=cat and evt.type=mmap)",
+		"not proc.name=cat or not evt.type=mmap");
+	ASSERT_FILTER_EQ(
+		"not (proc.name=cat and fd.type=file)",
+		"not proc.name=cat or not fd.type=file");
+	ASSERT_FILTER_EQ(
+		"not (evt.type=execve and evt.type=mmap)",
+		"not evt.type=execve or not evt.type=mmap");
+	ASSERT_FILTER_EQ(
+		"not (evt.type=mmap and evt.type=mmap)",
+		"not evt.type=mmap or not evt.type=mmap");
+
+	// negation isomorphism
+	ASSERT_FILTER_EQ("not evt.type=mmap", "evt.type!=mmap");
+	ASSERT_FILTER_EQ("not proc.name=cat", "proc.name!=cat");
+
+	// commutative property (and)
+	ASSERT_FILTER_EQ("evt.type=execve and evt.type=mmap", "evt.type=mmap and evt.type=execve");
+	ASSERT_FILTER_EQ("not (evt.type=execve and evt.type=mmap)", "not (evt.type=mmap and evt.type=execve)");
+	ASSERT_FILTER_EQ("not evt.type=execve and not evt.type=mmap", "not evt.type=mmap and not evt.type=execve");
+	ASSERT_FILTER_EQ("proc.name=cat and evt.type=mmap", "evt.type=mmap and proc.name=cat");
+	ASSERT_FILTER_EQ("not (proc.name=cat and evt.type=mmap)", "not (evt.type=mmap and proc.name=cat)");
+	ASSERT_FILTER_EQ("not proc.name=cat and not evt.type=mmap", "not evt.type=mmap and not proc.name=cat");
+	ASSERT_FILTER_EQ("proc.name=cat and fd.type=file", "fd.type=file and proc.name=cat");
+	ASSERT_FILTER_EQ("not (proc.name=cat and fd.type=file)", "not (fd.type=file and proc.name=cat)");
+	ASSERT_FILTER_EQ("not proc.name=cat and not fd.type=file", "not fd.type=file and not proc.name=cat");
+
+	// commutative property (or)
+	ASSERT_FILTER_EQ("evt.type=execve or evt.type=mmap", "evt.type=mmap or evt.type=execve");
+	ASSERT_FILTER_EQ("not (evt.type=execve or evt.type=mmap)", "not (evt.type=mmap or evt.type=execve)");
+	ASSERT_FILTER_EQ("not evt.type=execve or not evt.type=mmap", "not evt.type=mmap or not evt.type=execve");
+	ASSERT_FILTER_EQ("proc.name=cat or evt.type=mmap", "evt.type=mmap or proc.name=cat");
+	ASSERT_FILTER_EQ("not (proc.name=cat or evt.type=mmap)", "not (evt.type=mmap or proc.name=cat)");
+	ASSERT_FILTER_EQ("not proc.name=cat or not evt.type=mmap", "not evt.type=mmap or not proc.name=cat");
+	ASSERT_FILTER_EQ("proc.name=cat or fd.type=file", "fd.type=file or proc.name=cat");
+	ASSERT_FILTER_EQ("not (proc.name=cat or fd.type=file)", "not (fd.type=file or proc.name=cat)");
+	ASSERT_FILTER_EQ("not proc.name=cat or not fd.type=file", "not fd.type=file or not proc.name=cat");
+}