Terminology

ERG meaning representations are couched in Minimal Recursion Semantics (MRS; Copestake et al., 2005), which is conceptualized as a meta-language for the description of logical forms in a suitable object language. Formally, the meaning representations are triples 〈T, R, C〉, with T being the (global) top handle, R a set of elementary predications, and C a set of handle constraints.

Each elementary predication (EP) is comprised of a predicate symbol (henceforth simply predicate; an identifier of the relation) and a set of role–argument pairs, where the roles draw from a small, fixed inventory of role labels (ARG₀, …, ARG_n for ‘regular’ arguments; RSTR and BODY on generalized quantifiers; and a few others in more specialized constructions). Role values (i.e. arguments) are variables. Predicates can be optionally parameterized by one or more constant arguments.

Finally, handle constraints are an element of the MRS mechanics of scope underspecification, expressing a binary relation between two labels. The ERG limits itself to only one type of handle constraint, called ‘qeq’ (or =q), representing label equality modulo quantifier insertion.

Variable Types

There are three types of variables in MRS, event(ualitie)s (of type e), instances (of type x) and labels or handles (of type h). Of these, the latter serve a formalism-internal role, i.e. assuming a suitable variant of predicate logic as the object language, MRS labels do not map onto logical variables. Eventualities and instances, on the other hand, prototypically correspond to verbal and nominal expressions, respectively. In addition to these most specific variable types, there are underspecifications as follows: i (for individual) is a generalization over eventualities and instances; p (the half-way mark in the alphabet between h and x) is a generalization over labels and instances; and u (for unspecific or maybe unbound) generalizes over all of the above. Note that Copestake et al. (2001) use individual for what is called instance here.

Non-label variables can be ‘refined’ with what is called variable properties, e.g. TENSE or SF (sentence force) on eventualities, and NUM(ber) or PERS(on) on instances. Variable properties range over a fixed inventory of possible values, organized in a multiple-inheritance hierarchy to allow underspecification.

Intrinsic Arguments

In the ERG, all elementary predications have an ARG0 role, providing the intrinsic argument of a relation, e.g. the instance variable corresponding to a nominal expression, or the eventuality corresponding to a verbal expression in a (Neo-)Davidsonian representation. This intrinsic argument has also been referred to as the distinguished variable (Oepen & Lønning, 2006) or characteristic variable (Copestake 2009). We will at times say that a predication ‘introduces’ its intrinsic argument. Moreover, no variable will appear as the intrinsic argument of more than one predication in the semantic representation of an utterance.

For a blend of linguistic and technical reasons, the ERG also introduces intrinsic variables in the semantics of, among others, adjectives, adverbs, and prepositions–eventualities in all three cases (for further background, see the ErgSemantics/Design page).

Surface vs. Abstract Predicates (and Naming Conventions)

ERS predications are comprised of a predicate and a set of labeled arguments, e.g. something like

  h:_see_v_1[ARG0 e, ARG1 x1, ARG2 x2]

The predicate symbols can be divided into two classes: surface predicates and abstract predicates (where related terminology, with subtle variation in definitions used throughout the years, includes real vs. grammar predicates, as well as object-level vs. meta-level predicates, respectively).

Surface predicates follow a naming convention where the symbol is composed of three components, called lemma, pos, and sense, and the pos field (despite its morpho-syntactic name) serves to make top-level semantic sense distinctions that mostly align with a coarse inventory of word classes, e.g. ‘v’(erbal), ‘n’(ominal), or ‘q’(uantificational). Surface predicates, by convention, are marked by a leading underscore (‘_’; U+005F); as the finer-grained sense field is optional, this means that surface predicates will contain between two and three underscores, including the initial one. Surface predicates are exclusively introduced by lexical entries, whose orthography is a (possibly inflected) form of the lemma field in the predicate. Conversely, the vast majority of lexical entries introduce surface predicates.

Abstract predicates, on the other hand, constitute a smaller class. They are used to represent the semantic contribution of grammatical constructions or more specialized lexical entries (such as compounding or the comparative use of more, respectively). By convention abstract predicates must start with a character other than the underscore (but may include any number of underscores).

Predicate symbols (surface or abstract) are not case-sensitive and by convention are typically rendered in all lower-case letters.

Parameterized Relations

To avoid proliferation of predicates, some relations are parameterized, i.e. include a parameter (which technically is distinct from the arguments of the predication and typically will correspond to a constant in an object-language logic). Parameters are represented as case-sensitive strings. In the ERG at least, no relation takes more than one parameter.

For example, proper names are represented as follows in the ‘fingerprint language’ (see the ErgSemantics page for background):

  named(Abrams)[ARG0 x]

Conversely, in a popular serialization format for complete MRSs (the so-called simple MRS serialization; see the MrsRfc page), parameters are interspersed with regular arguments, using the (strictly speaking ERG-specific) pseudo-role label CARG:

  named[ARG0 x, CARG "Abrams"]

Terminology of Convenience

In describing the analyses in ERS, it is often convenient to refer to well-defined MRS fragments, i.e. interconnected groups of predications that do not necessarily constitute the full ERS for an utterance. In doing so, we differentiate between groups of predications ‘centered’ on an EP with an intrinsic variable of type e vs. those centered on an EP with an intrinsic variable of type x. As an informal terminology of convenience, we employ the terms situation and group for these, respectively.

Semi-formally, a situation on this view includes (a) the ‘main’ predication (prototypically contributed by a verb, but possibly by a preposition, adjective, adverb, or other syntactic category); (b) the full semantics of all of its arguments; and (c) the full semantics of all of its non-scopal modifiers. For example, in the semantic representation associated with Kim believes that Sandy probably left early., the situation centered on the believe EP includes the entire ERS; the one centered on the EP corresponding to probably the semantic contributions of probably, left, early, and Sandy; and that centered on the leave EP only the semantic contributions of left, early, and Sandy. Similarly, in the ERS for He was a loving husband. we can identify a situation centered on the love EP which includes the predications associated with loving, husband, and a.

Nearly analogously (and still quite informally), a group includes (a) the ‘main’ predication, introducing an intrinsic instance variable (here typically contributed by a noun); (b) the full semantics of any (non-scopal) modifiers of the noun (including complex ones, like relative clauses); (c) the quantifier predication which ‘binds’ the intrinsic variable of the ‘main’ predication; (d) the full semantics of any arguments of the ‘main’ predication, in the case of relational nouns. For example, in The dog that barked at that car slept., the group centered on dog includes the full ERS with the exception of the semantic contribution of slept; while the group centered on car includes only the semantic contributions of car and that.

We will call an operator any predication that takes at least one scopal (i.e. label-valued) argument, e.g. negation, and the relations introduced by scopal adverbs like probably, modal operators like must, and verbs like doubt. The scopal arguments of operators are always situations (in the current ERG), and the operator together with its argument(s) denotes a new (complex) situation.

Non-Scopal Arguments

Beyond its intrinsic argument, a predication can take additional arguments, for example to encode the two ‘participants’ in the two-place eat(ing) relation corresponding to an utterance like The girl ate an apple. Here, the two nominal arguments will each introduce a quantified instance variable, call them x₁ and x₂, which will be bound to the ARG1 and ARG2 roles in the predication introduced by eat. Non-label arguments (i.e. variables of types x or e, as well as of their underspecified supertype i) are called non-scopal, i.e. such variable bindings do not correspond to subordination (or a dominance relation) in the scope tree for an utterance.

Scopal Arguments

Arguments to predications that are of type h (i.e. a label) are called scopal arguments. These appear across a range of predication types, including quantifier predications which have scopal arguments for both their restriction (RSTR) and body (BODY) positions, and predications for verbs such as believe or ask which can embed situations, and other one- or two-place scopal operators such as not, probably, before, because, etc.

Quantification

The ERG assumes that all instance variables (of type x) are bound by a generalized quantifier, i.e. a predication whose ARG0 (or BV in some derived MRS views) is the instance variable, and whose restriction (RSTR) is the predication that has the variable as its intrinsic argument. As Copestake et al (2005) argue, the syntax of English leaves the body of quantifiers unconstrained and provides a partial constraint on the restriction, while the semantic contribution of the nominal constituent that a quantifier-predicate-introducing element attaches to in the syntax is required to be within the restriction of the quantifier. Thus in the ERG, the BODY of quantifier predications is left unconstrained, while the RSTR is linked to the semantic contribution of the nominal constituent, via a qeq constraint:

  h0:*[ARG0 x]
  [ARG0 x, RSTR h1]
  { h1 =q h0 }

More at [[ErgSemantics_Quantification]]

Non-Scopal Modification

Among non-scopal argument relations there is a distinguished class where the argument-taking predication shares its label (i.e. its position in the scope tree) with the predication that introduces the argument as its intrinsic argument. For example, the ERS for Every white cat is deaf includes the sub-structure

  h:_cat_n_1[ARG0 x]
  h:_white_a_1[ARG0 e, ARG1 x]

where x is the intrinsic argument of _cat_n_1 and the ARG1 of _white_a_1, and both predications share one label (viz. h). This type of configuration and its role in our analyses are described further on the ErgSemantics/Design page. When mapped to an object language, label sharing will typically correspond to logical conjunction, e.g. for the above something akin to cat(x) ∧ white(e, x).

We note here that scopal operators, whether introduced as heads or modifiers in the syntax, are indistinguishable in the semantics, and so from a semantic representation point of view, there is no such thing as a scopal modifier.

More Information

• ErgSemantics main page
• Inventory of semantic phenomena (to be) documented
• How to cite this work

References

Copestake, A., Flickinger, D., Pollard, C., & Sag, I. A. (2005). Minimal Recursion Semantics. An introduction. Research on Language and Computation, 3(2-3), pp. 281–332.

Copestake, A., Lascarides, A., & Flickinger, D. (2001). An algebra for semantic construction in constraint-based grammars. In Proceedings of the 39th Annual Meeting of the Association for Computational Linguistics (pp. 140–147). Toulouse, France.

Last update: 2023-08-27 by Alexandre Rademaker [edit]