PENMAN Notation

PENMAN notation, originally called Sentence Plan Notation in the PENMAN project ([KAS1989]), is a serialization format for the directed, rooted graphs used to encode semantic dependencies, most notably in the Abstract Meaning Representation (AMR) framework. It looks similar to Lisp’s S-Expressions in using parentheses to indicate nested structures. For example, here is an AMR for “He drives carelessly.”:

(d / drive-01
   :ARG0 (h / he)
   :manner (c / care-04
              :polarity -))

Described below are a breakdown of the parts of the PENMAN graph above as well as a formal grammar description of PENMAN graphs in general.

Graph Anatomy

The following diagram explains what each part of the graph above is:

;    ┌────────────────────────── Variable (this one is the graph's top)
;    │     ┌──────────────────── Instance relation
;    ┴ ────┴─────
    (d / drive-01
;      ┬ ───┬────
;      |    └─────────────────── Concept (node label)
;      └──────────────────────── Indicates the node's concept
;            ┌────────────────── Edge relation
;      ──────┴───────
       :ARG0 (h / he)
;      ──┬──
;        └────────────────────── Role (edge label)
       :manner (c / care-04
;                      ┌──────── Attribute relation
;                 ─────┴─────
                  :polarity -))
;                           ┬
;                           └─── Atom (or "constant")

The linearized form can only describe projective structures such as trees, so in order to capture non-projective graphs, nodes get identifiers (called variables; e.g., d, h, and c above) which can be referred to later to establish a reentrancy.

Formal Grammar

PENMAN notation can be very roughly described with the following BNF grammar (from [GOO2019]):

<node> ::= '(' <id> '/' <node-label> <edge>* ')'
<edge> ::= ':'<edge-label> (<const>|<id>|<node>)

A more complete description is given by the following PEG grammar. In addition to being more complete, it also extends the grammar to allow for surface alignments.

# Syntactic productions (whitespace is allowed around non-terminals)
Start     <- Node
Node      <- '(' Variable NodeLabel? Relation* ')'
NodeLabel <- '/' Concept Alignment?
Concept   <- Constant
Relation  <- Role Alignment? (Node / Atom Alignment?)
Atom      <- Variable / Constant
Constant  <- String / Symbol
Variable  <- Symbol

# Lexical productions (whitespace is not allowed)
Symbol    <- NameChar+
Role      <- ':' NameChar*
Alignment <- '~' ([a-zA-Z] '.'?)? Digit+ (',' Digit+)*
String    <- '"' (!'"' ('\\' . / .))* '"'
NameChar  <- ![ \n\t\r\f\v()/:~] .
Digit     <- [0-9]

This grammar has some seemingly unnecessary ambiguity in that both the Variable and Constant alternatives for Atom can resolve to Symbol, but it is written this way to accommodate syntax variants that further restrict the form of variables. Also, the distinction between edge relations and attribute relations is semantic: if the target of a relation is the variable of some other node, then it is an edge, otherwise it is an attribute.

Note that the implementation in the Penman package deviates from this grammar in that the Alignment production is not parsed together with the rest of the structure. Instead, the ~ character is allowed on NameChar and alignments are thus part of the Role or Atom tokens. They are later detected and extracted during graph interpretation (see penman.layout.interpret()).

KAS1989

Robert T. Kaspar. A Flexible Interface for Linking Applications to Penman’s Sentence Generator. Speech and Natural Language: Proceedings of a Workshop Held at Philadelphia, Pennsylvania. http://www.aclweb.org/anthology/H89-1022. February 21-23, 1989.

GOO2019

Michael Wayne Goodman. AMR Normalization for Fairer Evaluation. Proceedings of the 33rd Pacific Asia Conference on Language, Information, and Computation (PACLIC 33). https://arxiv.org/pdf/1909.01568.pdf. 2019.