Related papers: Interpolation in First-Order Logic
We show that several classes of ordered structures (namely, convex linear orders, layered permutations, and compositions) admit first-order logical limit laws.
We have recently presented a general method of proving the fundamental logical properties of Craig and Lyndon Interpolation (IPs) by induction on derivations in a wide class of internal sequent calculi, including sequents, hypersequents,…
Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…
We show that Propositional Dynamic Logic (PDL) has the Craig Interpolation Property. This question has been open for many years. Three proof attempts were published, but later criticized in the literature or retracted. Our proof is based on…
In \cite{Craig}, we introduced a syntactically defined and highly general class of calculi known as \emph{semi-analytic}. We then demonstrated that any sufficiently strong (modal) substructural logic with a semi-analytic calculus must…
The overall goal of this paper is to investigate the theoretical foundations of algorithmic verification techniques for first order linear logic specifications. The fragment of linear logic we consider in this paper is based on the linear…
We study the expressive power of successor-invariant first-order logic, which is an extension of first-order logic where the usage of an additional successor relation on the structure is allowed, as long as the validity of formulas is…
We consider a language together with the subword relation, the cover relation, and regular predicates. For such structures, we consider the extension of first-order logic by threshold- and modulo-counting quantifiers. Depending on the…
We present automated theorem provers for the first-order logic of here and there (HT). They are based on a native sequent calculus for the logic of HT and an axiomatic embedding of the logic of HT into intuitionistic logic. The analytic…
Quantifier elimination (QE) and Craig interpolation (CI) are central to various state-of-the-art automated approaches to hardware and software verification. They are rooted in the Boolean setting and are successful for, e.g., first-order…
In this article we show that bi-intuitionistic predicate logic lacks the Craig Interpolation Property. We proceed by adapting the counterexample given by Mints, Olkhovikov and Urquhart for intuitionistic predicate logic with constant…
Uniform interpolation properties are defined for equational consequence in a variety of algebras and related to properties of compact congruences on first the free and then the finitely presented algebras of the variety. It is also shown,…
The formal construction of the second-order logic or predicate calculus essentially adds quantifiers to propositional logic. Why second-order logic cannot be reduced to that of the first order? How to demonstrate that certain predicates are…
Logical reasoning is essential in a variety of human activities. A representative example of a logical task is mathematics. Recent large-scale models trained on large datasets have been successful in various fields, but their reasoning…
A sound and complete embedding of conditional logics into classical higher-order logic is presented. This embedding enables the application of off-the-shelf higher-order automated theorem provers and model finders for reasoning within and…
We uncover a close relationship between combinatorial and syntactic proofs for first-order logic (without equality). Whereas syntactic proofs are formalized in a deductive proof system based on inference rules, a combinatorial proof is a…
First-order iterative optimization methods play a fundamental role in large scale optimization and machine learning. This paper presents control interpretations for such optimization methods. First, we give loop-shaping interpretations for…
First-order probabilistic models combine representational power of first-order logic with graphical models. There is an ongoing effort to design lifted inference algorithms for first-order probabilistic models. We analyze lifted inference…
We investigate the properties of Inclusion Logic, that is, First Order Logic with Team Semantics extended with inclusion dependencies. We prove that Inclusion Logic is equivalent to Greatest Fixed Point Logic, and we prove that all…
We make three contributions. First, we formulate a discussion-graph semantics for first-order logic with equality, enabling reasoning about discussion and argumentation in AI more generally than before. This addresses the current lack of a…