Related papers: Craig Interpolation and Access Interpolation with …
We show that the guarded-negation fragment is, in a precise sense, the smallest extension of the guarded fragment with Craig interpolation. In contrast, we show that full first-order logic is the smallest extension of both the two-variable…
In this paper we develop cyclic proof systems for the problem of inclusion between the least sets of models of mutually recursive predicates, when the ground constraints in the inductive definitions belong to the quantifier-free fragments…
We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…
We lift the SCL calculus for first-order logic without equality to the SCL(T) calculus for first-order logic without equality modulo a background theory. In a nutshell, the SCL(T) calculus describes a new way to guide hierarchic resolution…
We present a method that allows efficient and safe approximation of model predictive controllers using kernel interpolation. Since the computational complexity of the approximating function scales linearly with the number of data points, we…
From tabulated nuclear and degenerate equations of state to photon and neutrino opacities, to nuclear reaction rates: tabulated data is ubiquitous in computational astrophysics. The dynamic range that must be covered by these tables…
We introduce a constructive method applicable to a large number of description logics (DLs) for establishing the concept-based Beth definability property (CBP) based on sequent systems. Using the highly expressive DL RIQ as a case study, we…
A new method for data-driven interpolatory model reduction is presented in this paper. Using the so-called data informativity perspective, we define a framework that enables the computation of moments at given (possibly complex)…
This paper defines the (first-order) conflict resolution calculus: an extension of the resolution calculus inspired by techniques used in modern SAT-solvers. The resolution inference is restricted to (first-order) unit-propagation and the…
We study uniform interpolation and forgetting in the description logic ALC. Our main results are model-theoretic characterizations of uniform inter- polants and their existence in terms of bisimula- tions, tight complexity bounds for…
The systematic method for the conversion of first class constraints to the equivalent set of Abelian one based on the Dirac equivalence transformation is developed. The representation for the corresponding matrix performing this…
Solving systems of polynomial equations, particularly those with finitely many solutions, is a crucial challenge across many scientific fields. Traditional methods like Gr\"obner and Border bases are fundamental but suffer from high…
Many applications of automated deduction require reasoning in first-order logic modulo background theories, in particular some form of integer arithmetic. A major unsolved research challenge is to design theorem provers that are "reasonably…
We consider the family of guarded and unguarded ordered logics, that constitute a recently rediscovered family of decidable fragments of first-order logic (FO), in which the order of quantification of variables coincides with the order in…
We introduce explicit families of good interpolation points for interpolation on a triangle in $\mathbb{R}^2$ that may be used for either polynomial interpolation or a certain rational interpolation for which we give explicit formulas.
We generalize the feasible interpolation theorem for semantic derivations from K.(1997) by allowing randomized protocols (protocols in the sense of K.(1997). We also introduce an extension of the monotone circuit model, monotone circuits…
We introduce first order alternating automata, a generalization of boolean alternating automata, in which transition rules are described by multisorted first order formulae, with states and internal variables given by uninterpreted…
The bisimulation proof method can be enhanced by employing `bisimulations up-to' techniques. A comprehensive theory of such enhancements has been developed for first-order (i.e., CCS-like) labelled transition systems (LTSs) and…
In logics with the Craig interpolation property (CIP) the existence of an interpolant for an implication follows from the validity of the implication. In logics with the projective Beth definability property (PBDP), the existence of an…
We bring an abstract model theory perspective to interpolation. We ask, what is the role of interpolation in the study of extensions of first order logic, such as infinitary logics, generalized quantifiers and higher order logics? The…