161,455 research outputs found
On Generalized Records and Spatial Conjunction in Role Logic
We have previously introduced role logic as a notation for describing
properties of relational structures in shape analysis, databases and knowledge
bases. A natural fragment of role logic corresponds to two-variable logic with
counting and is therefore decidable. We show how to use role logic to describe
open and closed records, as well the dual of records, inverse records. We
observe that the spatial conjunction operation of separation logic naturally
models record concatenation. Moreover, we show how to eliminate the spatial
conjunction of formulas of quantifier depth one in first-order logic with
counting. As a result, allowing spatial conjunction of formulas of quantifier
depth one preserves the decidability of two-variable logic with counting. This
result applies to two-variable role logic fragment as well. The resulting logic
smoothly integrates type system and predicate calculus notation and can be
viewed as a natural generalization of the notation for constraints arising in
role analysis and similar shape analysis approaches.Comment: 30 pages. A version appears in SAS 200
Higher-Order Horn Clauses
A generalization of Horn clauses to a higher-order logic is described and examined as a basis for logic programming. In qualitative terms, these higher-order Horn clauses are obtained from the first-order ones by replacing first-order terms with simply typed λ-terms and by permitting quantification over all occurrences of function symbols and some occurrences of predicate symbols. Several proof-theoretic results concerning these extended clauses are presented. One result shows that although the substitutions for predicate variables can be quite complex in general, the substitutions necessary in the context of higher-order Horn clauses are tightly constrained. This observation is used to show that these higher-order formulas can specify computations in a fashion similar to first-order Horn clauses. A complete theorem proving procedure is also described for the extension. This procedure is obtained by interweaving higher-order unification with backchaining and goal reductions, and constitutes a higher-order generalization of SLD-resolution. These results have a practical realization in the higher-order logic programming language called λProlog
One Quantifier Alternation in First-Order Logic with Modular Predicates
Adding modular predicates yields a generalization of first-order logic FO
over words. The expressive power of FO[<,MOD] with order comparison and
predicates for has been investigated by Barrington,
Compton, Straubing and Therien. The study of FO[<,MOD]-fragments was initiated
by Chaubard, Pin and Straubing. More recently, Dartois and Paperman showed that
definability in the two-variable fragment FO2[<,MOD] is decidable. In this
paper we continue this line of work.
We give an effective algebraic characterization of the word languages in
Sigma2[<,MOD]. The fragment Sigma2 consists of first-order formulas in prenex
normal form with two blocks of quantifiers starting with an existential block.
In addition we show that Delta2[<,MOD], the largest subclass of Sigma2[<,MOD]
which is closed under negation, has the same expressive power as two-variable
logic FO2[<,MOD]. This generalizes the result FO2[<] = Delta2[<] of Therien and
Wilke to modular predicates. As a byproduct, we obtain another decidable
characterization of FO2[<,MOD]
A functional tool for fuzzy first order logic evaluation
In this paper we present an automatic evaluation tool for fuzzy first order logic formulae. Since different logics can be considered, we allow for such formulae the appearance of syntactic modifiers, in such a way that our tool is designed not only to evaluate formulae in existing logic, but also to evaluate properties in any other logic framework given by the user. Such generalization is performed using Haskell, a functional programming language
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