When a new observation is added to an existing logical theory, it is often necessary to compute new consequences of this observation together with the theory. This paper investigates whether this reasoning task can be performed incrementally in a distributed setting involving first-order theories. We propose a complete asynchronous algorithm for this non-trivial task, and illustrate it with a s...

Craig interpolation is successfully used in both hardware and software model checking. An important class of state-of-the-art interpolation algorithms is based on recursive procedures that generate interpolants from refutations of unsatisfiable conjunctions of formulas. We analyze this type of algorithms and develop a theoretical framework, called a parametric interpolation framework, for arbit...

Fractional share models are used to reason about how multiple actors share ownership of resources. We examine the decidability and complexity of reasoning over the “tree share” model of Dockins et al. using first-order logic, or fragments thereof. We pinpoint a connection between the basic operations on trees union t, intersection u, and complement and countable atomless Boolean algebras, allow...

We introduce partially ordered two-way Büchi automata and characterize their expressive power in terms of fragments of first-order logic FO[<]. Partially ordered two-way Büchi automata are Büchi automata which can change the direction in which the input is processed with the constraint that whenever a state is left, it is never re-entered again. Nondeterministic partially ordered two-way Büchi ...

Many real world problems require a language at least as expressive as first order logic, yet there exist many barriers to the generation of first-order ontologies. One of the biggest hurdles is the specification of axioms that capture the intended semantics of a users concepts. This paper presents an ontology design algorithm enabled by modular ontology repositories that consist of theories org...

This work considers weak deterministic Büchi automata reading encodings of non-negative reals in a fixed base. A Real Number Automaton is an automaton which recognizes all encoding of elements of a set of reals. It is explained how to decide in linear time whether a set of reals recognized by a given minimal weak deterministic RNA is FO [R; +, <, 1]definable. Furthermore, it is explained how to...

A first-order theory T has the Schröder-Bernstein (SB) property if any pair of elementarily bi-embeddable models are isomorphic. We prove that T has an expansion by constants that has the SB property if and only if T is superstable and non-multidimensional. We also prove that among superstable theories T , the class of a-saturated models of T has the SB property if and only if T has no nomadic ...

In this paper, first-order logic is interpreted in the framework of universal algebra, using the clone theory developed in three previous papers [1] [2] and [3]. We first define the free clone T pL, Cq of terms of a first order language L over a set C of parameters in a standard way. The free right algebra FpL, Cq of formulas over the clone T pL, Cq of terms is then generated by atomic formulas...

Currently, adaptive educational hypermedia systems (AEHS) are described with nonuniform methods, depending on the specific view on the system, the application, or other parameters. There is no common language for expressing functionality of AEHS, hence these systems are difficult to compare and analyze. In this paper we investigate how a logical description can be employed to characterize adapt...

Hintikka and Sandu have developed IF logic as a genuine alternative to classical first-order logic: liberalizing dependence schemas between quantifiers, IF would carry out all the ideas already underlying classical logic. But they are alternatives to Hintikka’s game-theoretic approach; one could use instead Henkin quantifiers. We will present here some arguments of both technical and philosophi...