Related papers: Ground Canonicity
An abstract framework of canonical inference is used to explore how different proof orderings induce different variants of saturation and completeness. Notions like completion, paramodulation, saturation, redundancy elimination, and…
Induction in saturation-based first-order theorem proving is a new exciting direction in the automation of inductive reasoning. In this paper we survey our work on integrating induction directly into the saturation-based proof search…
We present a first-order theorem proving framework for establishing the correctness of functional programs implementing sorting algorithms with recursive data structures. We formalize the semantics of recursive programs in many-sorted…
Rewriting techniques based on reduction orderings generate "just enough" consequences to retain first-order completeness. This is ideal for superposition-based first-order theorem proving, but for at least one approach to inductive…
We consider a typical integration of induction in saturation-based theorem provers and investigate the effects of Skolem symbols occurring in the induction formulas. In a practically relevant setting we establish a Skolem-free…
We determine the proof-theoretic strength of the principle of countable saturation in the context of the systems for nonstandard arithmetic introduced in our earlier work.
For a few pairs $G\subset \hat G$ of reductive groups, we study the decomposition of irreducible $\hait G$-modules into $G$-modules. In particular, we observe the saturation property for all of these pairs.
Completion is one of the most studied techniques in term rewriting and fundamental to automated reasoning with equalities. In this paper we present new correctness proofs of abstract completion, both for finite and infinite runs. For the…
We present a survey of the saturation method for model-checking pushdown systems.
We present in this paper a new procedure to saturate a set of clauses with respect to a well-founded ordering on ground atoms such that A < B implies Var(A) {\subseteq} Var(B) for every atoms A and B. This condition is satisfied by any atom…
The saturation-based reasoning methods are among the most theoretically developed ones and are used by most of the state-of-the-art first-order logic reasoners. In the last decade there was a sharp increase in performance of such systems,…
We introduce layer systems for proving generalizations of the modularity of confluence for first-order rewrite systems. Layer systems specify how terms can be divided into layers. We establish structural conditions on those systems that…
Adding rewriting to a proof assistant based on the Curry-Howard isomorphism, such as Coq, may greatly improve usability of the tool. Unfortunately adding an arbitrary set of rewrite rules may render the underlying formal system undecidable…
Equality saturation is a powerful technique for program optimization. Contextual equality saturation extends this to support rewrite rules that are conditioned on where a term appears in an expression. Existing work has brought contextual…
Program analysis and verification require decision procedures to reason on theories of data structures. Many problems can be reduced to the satisfiability of sets of ground literals in theory T. If a sound and complete inference system for…
Redundancy elimination is one of the crucial ingredients of efficient saturation-based proof search. We improve redundancy elimination by introducing a new notion of redundancy, based on partial clauses and redundancy formulas, which is…
We import ideas from geometry to settle Sarnak's saturation problem for a large class of algebraic varieties.
We introduce a new covering property, defined in terms of order types of sequences of open sets, rather than in terms of cardinalities of families. The most general form of this compactness notion depends on two ordinal parameters. In the…
We generalize the notion of saturated order to infinite partial orders and give both a set-theoretic and an algebraic characterization of such orders. We then study the proof theoretic strength of the equivalence of these characterizations…
Modern saturation-based Automated Theorem Provers typically implement the superposition calculus for reasoning about first-order logic with or without equality. Practical implementations of this calculus use a variety of literal selections…