275 research outputs found
On Generalizing Decidable Standard Prefix Classes of First-Order Logic
Recently, the separated fragment (SF) of first-order logic has been
introduced. Its defining principle is that universally and existentially
quantified variables may not occur together in atoms. SF properly generalizes
both the Bernays-Sch\"onfinkel-Ramsey (BSR) fragment and the relational monadic
fragment. In this paper the restrictions on variable occurrences in SF
sentences are relaxed such that universally and existentially quantified
variables may occur together in the same atom under certain conditions. Still,
satisfiability can be decided. This result is established in two ways: firstly,
by an effective equivalence-preserving translation into the BSR fragment, and,
secondly, by a model-theoretic argument.
Slight modifications to the described concepts facilitate the definition of
other decidable classes of first-order sentences. The paper presents a second
fragment which is novel, has a decidable satisfiability problem, and properly
contains the Ackermann fragment and---once more---the relational monadic
fragment. The definition is again characterized by restrictions on the
occurrences of variables in atoms. More precisely, after certain
transformations, Skolemization yields only unary functions and constants, and
every atom contains at most one universally quantified variable. An effective
satisfiability-preserving translation into the monadic fragment is devised and
employed to prove decidability of the associated satisfiability problem.Comment: 34 page
A Type-coherent, Expressive Representation as an Initial Step to Language Understanding
A growing interest in tasks involving language understanding by the NLP
community has led to the need for effective semantic parsing and inference.
Modern NLP systems use semantic representations that do not quite fulfill the
nuanced needs for language understanding: adequately modeling language
semantics, enabling general inferences, and being accurately recoverable. This
document describes underspecified logical forms (ULF) for Episodic Logic (EL),
which is an initial form for a semantic representation that balances these
needs. ULFs fully resolve the semantic type structure while leaving issues such
as quantifier scope, word sense, and anaphora unresolved; they provide a
starting point for further resolution into EL, and enable certain structural
inferences without further resolution. This document also presents preliminary
results of creating a hand-annotated corpus of ULFs for the purpose of training
a precise ULF parser, showing a three-person pairwise interannotator agreement
of 0.88 on confident annotations. We hypothesize that a divide-and-conquer
approach to semantic parsing starting with derivation of ULFs will lead to
semantic analyses that do justice to subtle aspects of linguistic meaning, and
will enable construction of more accurate semantic parsers.Comment: Accepted for publication at The 13th International Conference on
Computational Semantics (IWCS 2019
Efficient elimination of Skolem functions in
Elimination of a single Skolem function in pure logic increases the length of
proofs only linearly. The result is shown for derivations with cuts that are
free for the Skolem function in a sequent calculus with strong locality
property.Comment: 31 pages; generalization of main results for calculus with cuts,
added section on cut elimination, added discussion on eigenvariable conditio
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