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Complexity of the Two-Variable Fragment with Counting Quantifiers
The satisfiability and finite satisfiability problems for the two-variable fragment of first-order logic with counting quantifiers are both in NEXPTIME, even when counting quantifiers are codedExpand
On the Computational Complexity of the Numerically Definite Syllogistic and Related Logics
TLDR
The related problem of probabilistic (propositional) satisfiability is discussed, and the incompleteness of some proof-systems that have been proposed for the numerically definite syllogistic are demonstrated. Expand
Fragments of Language
TLDR
This paper represents a casestudy in how to approach the problem of determining the logicalcomplexity of various natural language constructions, and draws some general conclusions about the relationship between naturallanguage and formal logic. Expand
More Fragments of Language
TLDR
The present paper considers various fragments of English involving ditransitive verbs and determines their semantic complexity. Expand
Data-complexity of the two-variable fragment with counting quantifiers
The data-complexity of both satisfiability and finite satisfiability for the two-variable fragment with counting quantifiers is NP-complete; the data-complexity of both query answering and finiteExpand
A Note on the Complexity of the Satisfiability Problem for Graded Modal Logics
TLDR
Tight complexity bounds are obtained for the problem of determining the satisfiability of a given graded modal logic formula over the classes of frames characterized by any combination of reflexivity, seriality, symmetry, transitivity and the Euclidean property. Expand
Temporal prepositions and their logic
TLDR
It is shown that the satisfiability problem for TPL is NEXPTIME-complete and the phrase-structures which this grammar assigns to the sentences it recognizes can be viewed as formulas of an interval temporal logic whose satisfaction-conditions faithfully represent the meanings of the corresponding English sentences. Expand
A Two-Variable Fragment of English
TLDR
This paper defines a controlled language, E2V, whose principalgrammatical resources include determiners, relative clauses, reflexives and pronouns, and provides a formal syntax and semantics for E1V, in whichanaphoric ambiguities are resolved in a linguistically natural way. Expand
The Two-Variable Fragment with Counting Revisited
TLDR
This paper presents a simplified proof via a result on integer programming due to Eisenbrand and Shmonina of the satisfiability and finite satisfiability problems for the two-variable fragment of first-order logic with counting. Expand
A Complete Axiom System for Polygonal Mereotopology of the Real Plane
TLDR
A calculus for mereotopological reasoning in which two-dimensional spatial regions are treated as primitive entities in which polygonal open subsets of the real plane serve as elements of the domain is presented. Expand
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