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ErgSemantics_Basics
ERG meaning representations are couched in Minimal Recursion Semantics (MRS; Copestake et al 2005), which in turn is conceptualized as a metalanguage for describing logical forms in some 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 predication) and a set of role–argument pairs, where the roles draw from a small, fixed inventory of role labels (ARG0, ..., ARGn 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.
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 (called individual) is a supertype of eventualities and instances; p (the half-way mark in the alphabet between h and x) is a supertype of labels and instances; and u (for unspecific or maybe unbound) is a supertype of all of the above. Note that Copestake et al (2001) use the term individual where we use instance. As there is no previously established term for the abstraction over e and x, we have reclaimed individual for that purpose.
Non-label variables can be ‘refined’ with what we call 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.
In the ERG, all elementary predications have an ARG0 role, providing the intrinsic argument of a relation, e.g. the instance variable introduced by the semantics of a nominal expression, or the eventuality corresponding to the semantics of a verbal expression in a (Neo-)Davidsonian representation. This intrinsic argument is at times also refered 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.
For what is quite likely 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.
MRS predications are comprised of a relation symbol and a set of labeled arguments, e.g. something like
h:_see_v_1[ARG0 e, ARG1 x1, ARG2 x2]
Here, _see_v_1 names the two-place relation corresponding to the verb see, and the predicate name is by convention composed of three components, called lemma, pos, and sense, where 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), ‘p’(repositional), or ‘q’(uantificational).
This decomposition of predicate names, however, only applies to so-called surface predicates, i.e. ones that are part of the semantics of a lexical entry whose orthography includes the (possibly inflected) lemma value; this is the default for the vast majority of lexical entries. All other predicates, e.g. those associated with the semantics of grammatical constructions or more specialized lexical entries (like the comparative use of more) we call abstract predicates. Related terminology, with subtle variation in definitions, that has been used in the context of MRS and DELPH-IN grammars throughout the years include real and grammar, as well as object-level and meta-level predicate, for surface and abstract predicates, respectively.
Surface predicates, by convention, are marked by a leading underscore (‘_’; U+005F); as the sense field is optional, this means that surface predicates will contain between two and three underscores, including the initial one; abstract predicates, on the other hand, can include any number of underscores, but must start in a character other than the underscore. Predicate names are not case-sensitive and by convention typically rendered in all lowercase letters.
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:
named(Abrams)[ARG0 x]
In the so-called simple MRS serialization (which is not the fingerprint language), parameters are interspersed with regular arguments, using the pseudo-role label CARG:
named[ARG0 x, CARG "Abrams"]
To refer to various types of MRS fragments, i.e. interconnected groups of predications, we will at times use the term situation to refer to the semantics associated with a verbal projection, i.e. various types of clauses. The complete MRS associated with a (declarative) sentence, for example, denotes a situation, as do the predications associated with a participial attributive modifier, say in He was a loving husband. Semi-formally, a situation on this view includes (a) the ‘main’ predication (typically contributed by a verb); (b) the full semantics of all its arguments; and (c) the full semantics of all its intersective modifiers.
We will call an operator any predication that takes at least one scopal (i.e. label-valued) argument, e.g. negation, scopal adverbs like probably, modal operators like must, and the relations introduced by verbs like doubt. The scopal arguments of operators are situations, and the operator together with its argument(s) denotes a new (complex) situation.
The semantics corresponding to nominals prototypically involves an instance variable and a (generalized) quantifier, which jointly we take to denote a set, possibly one of singleton cardinality (for quantifiers introduced by singular determiners, e.g. a or this) or even an empty set (for the no quantifier, as in for example no dogs bark).
Beyond its intrinsic argument, a predication can take additional arguments, for example to encode the two ‘participants’ in the two-place ‘eating’ 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 hierarchy.
Arguments to predications that are of type h (i.e. a label)
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. To allow insertion of other quantifier in scope resolution, the restriction is linked to the predication ‘introducing’ the variable:
h0:*[ ARG0 x ]
[ ARG0 x, RSTR h1 ]
{ h1 =q h0 }
predicated of an event or instance and sharing label (i.e. position in the scope hierarchy).
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ErgSemantics main page
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Inventory of semantic phenomena (to be) documented
Copestake, A., Flickinger, D., Pollard, C., & Sag, I. A. (2005). Minimal recursion semantics: An introduction. Research on Language and Computation, 3(2-3), 281-332.
Copestake, A., Lascarides, A., & Flickinger, D. (2001, July). An algebra for semantic construction in constraint-based grammars. In Proceedings of the 39th Annual Meeting on Association for Computational Linguistics (pp. 140-147). Association for Computational Linguistics.
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