We analyze the logical form of the domain knowledge that grounds analogical inferences and generalizations from a single instance. The form of the assumptions which justify analogies is given schematically as the "determination rule", so called because it expresses the relation of one set of variables determining the values of another set. The determination relation is a logical generalization ...

Generic rst-order logic (GFOL) is a rst-order logic parameterized with terms de ned axiomatically (rather than constructively), by requiring them to only provide generic notions of free variable and substitution satisfying reasonable properties. GFOL has a complete Gentzen system generalizing that of FOL. An important fragment of GFOL, called HORN, possesses a much simpler Gentzen system, simil...

We introduce a first-order language for semantic underspecification that we call Constraint Language for Lambda-Structures (CLLS). A A-structure can be considered as a A-term up to consistent renaming of bound variables (a-equality); a constraint of CLLS is an underspec-ified description of a A-structure. CLLS solves a capturing problem omnipresent in underspec-ified scope representations. CLLS...

The story goes back to 1940, with the publication of Quine's Mathematical Logic [5]. He there presents a system of quantificational logic in which only sentences or closed formulas are theorems. In that system, the sole rule of inference is Modus Ponens and the axioms are the universal closures of the following formulas: (1) $, for @ tautologous; (2) Wvb) 1 vcwv~~); (3) qb 3 Vcuj, for o not fre...

We present a variant of the Davis–Fechter’s technique for eliminating quantifiers in first-order logic, aimed at reducing the incidence of irrelevant dependencies in the construction of Skolem terms. The basic idea behind this contribution is to treat as a single syntactic unit every maximal ‘quantifier batch’, i.e., group of contiguous alike quantifiers, whose internal order (which has no sign...

A formalism for constructing and using axiomatic specifications in an arbitrary logical system is presented. This builds on the framework provided by Goguen and Burstall’s work on the notion of an institution as a formalisation of the concept of a logical system for writing specifications. We show how to introduce free variables into the sentences of an arbitrary institution and how to add quan...

This article discusses graphical models that can handle latent variables without explicitly modeling them quantitatively. There exist several paradigms for such problem domains. Two of them are semi-Markovian causal models and maximal ancestral graphs. Applying these techniques to a problem domain consists of several steps, typically: structure learning from observational and experimental data,...

We describe the construction and use of a system for translating higher order logic-based speciications into programs in the higher order logic programming language Lambda Prolog. The translation improves on previous work in the eld of executing speciications by allowing formulas with quantiiers to be executed, and by permitting users to pose Prolog-style queries with free variables to be insta...

We study a class of first-order theories whose complete quantifier-free types with one free variable either have a trivial positive part or are isolated by a positive quantifier-free formula—plus a few other technical requirements. The theory of vector spaces and the theory fields are examples. We prove the amalgamation property and the existence of a model-companion. We show that the model-com...