Related papers: Second-Order Functions and Theorems in ACL2
The class of type-two basic feasible functionals ($\mathtt{BFF}_2$) is the analogue of $\mathtt{FP}$ (polynomial time functions) for type-2 functionals, that is, functionals that can take (first-order) functions as arguments.…
Fundamentally, every static program analyser searches for a proof through a combination of heuristics providing candidate solutions and a candidate validation technique. Essentially, the heuristic reduces a second-order problem to a…
Many automatic theorem-provers rely on rewriting. Using theorems as rewrite rules helps to simplify the subgoals that arise during a proof. LCF is an interactive theorem-prover intended for reasoning about computation. Its implementation of…
Even though the ACL2 logic is first order, the ACL2 system offers several mechanisms providing users with some operations akin to higher order logic ones. In this paper, we propose a macro, named instance-of-defspec, to ease the reuse of…
Understanding the role of citations is essential for research assessment and citation-aware digital libraries. However, existing citation classification frameworks often conflate citation intent (why a work is cited) with cited content type…
Semantic parsing is the task of obtaining machine-interpretable representations from natural language text. We consider one such formal representation - First-Order Logic (FOL) and explore the capability of neural models in parsing English…
We present a new approach to automated reasoning about higher-order programs by endowing symbolic execution with a notion of higher-order, symbolic values. Our approach is sound and relatively complete with respect to a first-order solver…
In this paper we give an ordinal analysis of the theory of second order arithmetic. We do this by working with proof trees -- that is, "deductions" which may not be well-founded. Working in a suitable theory, we are able to represent…
Skolem functions play a central role in the study of first order logic, both from theoretical and practical perspectives. While every Skolemized formula in first-order logic makes use of Skolem constants and/or functions, not all such…
Optimization in machine learning, both theoretical and applied, is presently dominated by first-order gradient methods such as stochastic gradient descent. Second-order optimization methods, that involve second derivatives and/or second…
The purpose of this work is to complete the algebraic foundations of second-order languages from the viewpoint of categorical algebra as developed by Lawvere. To this end, this paper introduces the notion of second-order algebraic theory…
The theory of asymptotic complexity provides an approach to characterizing the behavior of programs in terms of bounds on the number of computational steps executed or use of computational resources. We describe work using ACL2 to prove…
We present a mechanized embedding of higher-order logic (HOL) and algebraic data types (ADT) into first-order logic with ZFC axioms. We implement this in the Lisa proof assistant for schematic first-order logic and its library based on…
Second-order quantifier-elimination is the problem of finding, given a formula with second-order quantifiers, a logically equivalent first-order formula. While such formulas are not computable in general, there are practical algorithms and…
We propose a novel logic, called Frame Logic (FL), that extends first-order logic (with recursive definitions) using a construct Sp(.) that captures the implicit supports of formulas -- the precise subset of the universe upon which their…
With the rapid adoption of machine learning systems in sensitive applications, there is an increasing need to make black-box models explainable. Often we want to identify an influential group of training samples in a particular test…
Functions with fixed initial coefficient have been widely studied. A new methodology is proposed in this paper by making appropriate modifications and improvements to the theory of second-order differential subordination. Several…
This talk describes how a combination of symbolic computation techniques with first-order theorem proving can be used for solving some challenges of automating program analysis, in particular for generating and proving properties about the…
Higher-order logic programming is an interesting extension of traditional logic programming that allows predicates to appear as arguments and variables to be used where predicates typically occur. Higher-order characteristics are indeed…
The idea of using unfolding as a way of computing a program semantics has been applied successfully to logic programs and has shown itself a powerful tool that provides concrete, implementable results, as its outcome is actually source…