Related papers: Symbolic Model Construction for Saturated Constrai…
This paper obtains a completeness result for inequational reasoning with applicative terms without variables in a setting where the intended semantic models are the full structures, the full type hierarchies over preorders for the base…
We consider a class of formula equations in first-order logic, Horn formula equations, which are defined by a syntactic restriction on the occurrences of predicate variables. Horn formula equations play an important role in many…
We present a method for verifying the correctness of imperative programs which is based on the automated transformation of their specifications. Given a program prog, we consider a partial correctness specification of the form $\{\varphi\}$…
Bounded model finding is a key technique for validating software designs, usually obtained by translating high-level specifications into SAT/SMT problems. Although effective, such translations introduce a semantic gap and a dependency on…
In this paper, we explore the task of automatically generating natural language descriptions of salient patterns in a time series, such as stock prices of a company over a week. A model for this task should be able to extract high-level…
Horn clauses and first-order resolution are commonly used to implement type classes in Haskell. Several corecursive extensions to type class resolution have recently been proposed, with the goal of allowing (co)recursive dictionary…
Definition Modeling, the task of generating definitions, was first proposed as a means to evaluate the semantic quality of word embeddings-a coherent lexical semantic representations of a word in context should contain all the information…
Verification problems of programs written in various paradigms (such as imperative, logic, concurrent, functional, and object-oriented ones) can be reduced to problems of solving Horn clause constraints on predicate variables that represent…
Building on the successes of satisfiability modulo theories (SMT), Bj{\o}rner et al. initiated a research programme advocating Horn constraints as a suitable basis for automatic program verification. The notion of first-order constrained…
We establish new, and surprisingly tight, connections between propositional proof complexity and finite model theory. Specifically, we show that the power of several propositional proof systems, such as Horn resolution, bounded-width…
The underlying structure of natural language is hierarchical; words combine into phrases, which in turn form clauses. An awareness of this hierarchical structure can aid machine learning models in performing many linguistic tasks. However,…
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 constraint satisfaction problem (CSP) of a first-order theory T is the computational problem of deciding whether a given conjunction of atomic formulas is satisfiable in some model of T. We study the computational complexity of CSP$(T_1…
We consider approximating data structures with collections of the items that they contain. For examples, lists, binary trees, tuples, etc, can be approximated by sets or multisets of the items within them. Such approximations can be used to…
Definitions of new symbols merely abbreviate expressions in logical frameworks, and no new facts (regarding previously defined symbols) should hold because of a new definition. In Isabelle/HOL, definable symbols are types and constants. The…
We propose an efficient interpretable neuro-symbolic model to solve Inductive Logic Programming (ILP) problems. In this model, which is built from a set of meta-rules organised in a hierarchical structure, first-order rules are invented by…
We explore using latent natural language instructions as an expressive and compositional representation of complex actions for hierarchical decision making. Rather than directly selecting micro-actions, our agent first generates a latent…
In this paper, we study the problem of generating inputs to a higher-order program causing it to error. We first study the problem in the setting of PCF, a typed, core functional language and contribute the first relatively complete method…
Human beings possess the most sophisticated computational machinery in the known universe. We can understand language of rich descriptive power, and communicate in the same environment with astonishing clarity. Two of the many contributors…
In this paper we linearise the recently introduced geometrically nonlinear constrained Cosserat-shell model. In the framework of the linear constrained Cosserat-shell model, we provide a comparison of our linear models with the classical…