Related papers: Lloyd-Topor Completion and General Stable Models
Recent developments in termination analysis for declarative programs emphasize the use of appropriate models for the logical theory representing the program at stake as a generic approach to prove termination of declarative programs. In…
We present a new approach to termination analysis of logic programs. The essence of the approach is that we make use of general orderings (instead of level mappings), like it is done in transformational approaches to logic program…
We rewrite simplicially the standard definitions of a complete first order theory, a model of it, and various characterisations of stability of a complete first order theory. In our reformulations the simplicial language replaces the…
In 1967 the author introduced a pre-ordering of all first order complete theories where T is lower than U if it is easier for an ultrapower of a model of T than an ultrapower of a model of U to be saturated. In a long series of recent…
We investigate the decidability of the definability problem for fragments of first order logic over finite words enriched with modular predicates. Our approach aims toward the most generic statements that we could achieve, which…
This paper involves generalizing the Goldblatt-Thomason and the Lindstr\"om characterization theorems to first-order modal logic.
It is well known that, under certain conditions, it is possible to split logic programs under stable model semantics, i.e. to divide such a program into a number of different "levels", such that the models of the entire program can be…
We describe the notion of stability of coherent systems as a framework to deal with redundancy. We define stable coherent systems and show how this notion can help the design of reliable systems. We demonstrate that the reliability of…
Recently, symbolic structures were proposed as finite representations of potentially infinite first-order structures, where Linear Integer Arithmetic terms and formulas define the domain and interpretations of a structure. We generalize…
We know extensions of first order logic by quantifiers of the kind "there are uncountable many ...", "most ..." with new axioms and appropriate semantics. Related are operations such as "set of x, such that ...", Hilbert's…
The module theorem by Janhunen et al. demonstrates how to provide a modular structure in answer set programming, where each module has a well-defined input/output interface which can be used to establish the compositionality of answer sets.…
Tarski gave a general semantics for deductive reasoning: a formula a may be deduced from a set A of formulas iff a holds in all models in which each of the elements of A holds. A more liberal semantics has been considered: a formula a may…
Modern distributed systems often achieve availability and scalability by providing consistency guarantees about the data they manage weaker than linearizability. We consider a class of such consistency models that, despite this weakening,…
In this paper we give a new proof for the completeness of infinite valued propositional \L ukasiewicz logic introduced by \L ukasiewicz and Tarski in 1930. Our approach employs a Hilbert-style proof that relies on the concept of maximal…
We derive normal approximation results for a class of stabilizing functionals of binomial or Poisson point process, that are not necessarily expressible as sums of certain score functions. Our approach is based on a flexible notion of the…
In this article we formally define and investigate the computational complexity of the Definability Problem for open first-order formulas (i.e., quantifier free first-order formulas) with equality. Given a logic $\mathbf{\mathcal{L}}$, the…
PCF is a sequential simply typed lambda calculus language. There is a unique order-extensional fully abstract cpo model of PCF, built up from equivalence classes of terms. In 1979, G\'erard Berry defined the stable order in this model and…
Monadic second order logic and linear temporal logic are two logical formalisms that can be used to describe classes of infinite words, i.e., first-order models based on the natural numbers with order, successor, and finitely many unary…
In this paper, we investigate how the initial models and the final models for the polynomial functors can be uniformly specified in matching logic.
We introduce and study logic programs whose clauses are built out of monotone constraint atoms. We show that the operational concept of the one-step provability operator generalizes to programs with monotone constraint atoms, but the…