Related papers: Efficiently Simulating Higher-Order Arithmetic by …

We introduce a class of first-order methods for smooth constrained optimization that are based on an analogy to non-smooth dynamical systems. Two distinctive features of our approach are that (i) projections or optimizations over the entire…

This note discusses proofs for convergence of first-order methods based on simple potential-function arguments. We cover methods like gradient descent (for both smooth and non-smooth settings), mirror descent, and some accelerated variants.

This paper discusses the method of formative rules for first-order term rewriting, which was previously defined for a higher-order setting. Dual to the well-known usable rules, formative rules allow dropping some of the term constraints…

We continue our investigation into hybrid polyadic multi-sorted logic with a focus on expresivity related to the operational and axiomatic semantics of rogramming languages, and relations with first-order logic. We identify a fragment of…

Grounding is the task of reducing a first-order theory and finite domain to an equivalent propositional theory. It is used as preprocessing phase in many logic-based reasoning systems. Such systems provide a rich first-order input language…

This paper presents matching logic, a first-order logic (FOL) variant for specifying and reasoning about structure by means of patterns and pattern matching. Its sentences, the patterns, are constructed using variables, symbols, connectives…

It is commonly agreed that the success of future proof assistants will rely on their ability to incorporate computations within deduction in order to mimic the mathematician when replacing the proof of a proposition P by the proof of an…

This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…

We give a simple and direct proof that super-consistency implies the cut elimination property in deduction modulo. This proof can be seen as a simplification of the proof that super-consistency implies proof normalization. It also takes…

This paper investigates first-order game logic and first-order modal mu-calculus, which extend their propositional modal logic counterparts with first-order modalities of interpreted effects such as variable assignments. Unlike in the…

The univalence axiom expresses the principle of extensionality for dependent type theory. However, if we simply add the univalence axiom to type theory, then we lose the property of canonicity - that every closed term computes to a…

We present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…

Many classical planning frameworks are built on first-order languages. The first-order expressive power is desirable for compactly representing actions via schemas, and for specifying quantified conditions such as $\neg\exists…

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 consider a first-order logic for the integers with addition. This logic extends classical first-order logic by modulo-counting, threshold-counting and exact-counting quantifiers, all applied to tuples of variables (here, residues are…

Goal-directed proof search in first-order logic uses meta-variables to delay the choice of witnesses; substitutions for such variables are produced when closing proof-tree branches, using first-order unification or a theory-specific…

We address generating theorems from a given set of axioms, without proof goal, aiming at value from a mathematical point of view or as lemmas for automated proving. As benchmark, we convert a fragment of the Metamath database set.mm. Our…

Representing a proof tree by a combinator term that reduces to the tree lets subtle forms of duplication within the tree materialize as duplicated subterms of the combinator term. In a DAG representation of the combinator term these…

Exactly solving first-order constraints (i.e., first-order formulas over a certain predefined structure) can be a very hard, or even undecidable problem. In continuous structures like the real numbers it is promising to compute approximate…

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…