Categories with families and first-order logic with dependent sorts

First Order Logic with Dependent

First-Order Logic with Dependent Types

We present DFOL, an extension of classical first-order logic with dependent types, i.e., as in Martin-Löf type theory, signatures may contain type-valued function symbols. A model theory for the logic is given that stays close to the established first-order model theory. The logic is presented as an institution, and the logical framework LF is used to define signatures, terms and formulas. We s...

Computing with First-Order Logic

We study two important extensions of rst-order logic (FO) with iteration, the xpoint and while queries. The main result of the paper concerns the open problem of the relationship between xpoint and while: they are the same ii ptime = pspace. These and other expressibility results are obtained using a powerful normal form for while which shows that each while computation over an unordered domain...

the past hospitalization and its association with suicide attempts and ideation in patients with mdd and comparison with bmd (depressed type) group

چکیده ندارد.

Non-cyclic Sorts for First-Order Satisfiability

In this paper we investigate the finite satisfiability problem for firstorder logic. We show that the finite satisfiability problem can be represented as a sequence of satisfiability problems in a fragment of many-sorted logic, which we call the non-cyclic fragment. The non-cyclic fragment can be seen as a generalisation of the effectively propositional fragment (EPR) in the many-sorted setting...