Adding For-Loops to First-Order Logic

Adding Metatheoretic Facilities to First-Order Theories

Generic proof systems like Isabelle provide some limited but useful metatheoretic facilities for declared logics; in particular, users can prove simple derived rules and alsòsolve' formulae that contain metavariables | a technique useful for, e.g., program synthesis. We show how an arbitrary rst order theory can be conservatively extended to provide similar facilities, without a supporting meta...

From Separation Logic to First-Order Logic

Separation logic is a spatial logic for reasoning locally about heap structures. A decidable fragment of its assertion language was presented in [1], based on a bounded model property. We exploit this property to give an encoding of this fragment into a first-order logic containing only the propositional connectives, quantification over the natural numbers and equality. This result is the first...

Adding Numbers to the SHIQ Description Logic: First Results

Beyond First Order Logic: From number of structures to structure of numbers: Part I

We study the history and recent developments in nonelementarymodel theory focusing on the framework of abstractelementary classes. We discuss the role of syntax and semanticsand the motivation to generalize first order model theory to nonelementaryframeworks and illuminate the study with concrete examplesof classes of models. This first part introduces the main conceps and philosophies anddiscu...

Beyond first order logic: From number of structures to structure of numbers: Part II

We study the history and recent developments in nonelementarymodel theory focusing on the framework of abstractelementary classes. We discuss the role of syntax and semanticsand the motivation to generalize first order model theory to nonelementaryframeworks and illuminate the study with concrete examplesof classes of models. This second part continues to study the question of catecoricitytrans...