Only install the liblognorm.h header, others look like private headers.
Use _SOURCES for those instead of _HEADERS / EXTRA_DIST.

Index: src/Makefile.am
--- src/Makefile.am.orig
+++ src/Makefile.am
@@ -24,23 +24,32 @@ lib_LTLIBRARIES = liblognorm.la
 liblognorm_la_SOURCES = \
 	liblognorm.c \
 	pdag.c \
+	pdag.h \
 	annot.c \
+	annot.h \
 	samp.c \
+	samp.h \
 	lognorm.c \
+	lognorm.h \
 	parser.c \
+	parser.h \
 	enc_syslog.c \
 	enc_csv.c \
-	enc_xml.c
+	enc_xml.c \
+	enc.h \
+	lognorm-features.h \
+	helpers.h \
+	internal.h
 
 # Users violently requested that v2 shall be able to understand v1
 # rulebases. As both are very very different, we now include the
 # full v1 engine for this purpose. This here is what does this.
 # see also: https://github.com/rsyslog/liblognorm/issues/103
 liblognorm_la_SOURCES += \
-	v1_liblognorm.c \
-	v1_parser.c \
-	v1_ptree.c \
-	v1_samp.c
+	v1_liblognorm.c v1_liblognorm.h \
+	v1_parser.c v1_parser.h \
+	v1_ptree.c v1_ptree.h \
+	v1_samp.c v1_samp.h
 
 liblognorm_la_CPPFLAGS = $(JSON_C_CFLAGS) $(WARN_CFLAGS) $(LIBESTR_CFLAGS) $(PCRE_CFLAGS)
 liblognorm_la_LIBADD = $(rt_libs) $(JSON_C_LIBS) $(LIBESTR_LIBS) $(PCRE_LIBS) -lestr
@@ -49,22 +58,5 @@ liblognorm_la_LIBADD = $(rt_libs) $(JSON_C_LIBS) $(LIB
 # Note: v2 now starts at version 5, as v1 previously also had 4
 liblognorm_la_LDFLAGS = -version-info 6:0:1
 
-EXTRA_DIST = \
-	internal.h \
-	liblognorm.h \
-	lognorm.h \
-	pdag.h \
-	annot.h \
-	samp.h \
-	enc.h \
-	parser.h \
-	helpers.h
-
-# and now the old cruft:
-EXTRA_DIST += \
-	v1_liblognorm.h \
-	v1_parser.h \
-	v1_samp.h \
-	v1_ptree.h
-
-include_HEADERS = liblognorm.h samp.h lognorm.h pdag.h annot.h enc.h parser.h lognorm-features.h
+# Public API
+include_HEADERS = liblognorm.h