Related papers: Synthesising Recursive Functions for First-Order M…
Superposition is an established decision procedure for a variety of first-order logic theories represented by sets of clauses. A satisfiable theory, saturated by superposition, implicitly defines a minimal term-generated model for the…
In this paper, we propose a general framework in continual learning for generative models: Feature-oriented Continual Learning (FoCL). Unlike previous works that aim to solve the catastrophic forgetting problem by introducing regularization…
We determine sufficient conditions under which certain recursively defined functions are well defined for all real inputs. Given a function $f:\mathbb R\to\mathbb R$, call a decreasing sequence $x_1>x_2>x_3>\cdots$ "$f$-bad" if…
We study the reactive synthesis problem for distributed systems with an unbounded number of participants interacting with an uncontrollable environment. Executions of those systems are modeled by data words, and specifications are given as…
Reasoning in language models is difficult to evaluate: natural-language traces are unverifiable, symbolic datasets are too small, and most benchmarks conflate heuristics with inference. We present FOL-Traces, the first large-scale dataset…
Standard gradient descent methods are susceptible to a range of issues that can impede training, such as high correlations and different scaling in parameter space.These difficulties can be addressed by second-order approaches that apply a…
Accelerated first order methods, also called fast gradient methods, are popular optimization methods in the field of convex optimization. However, they are prone to suffer from oscillatory behaviour that slows their convergence when medium…
In this paper, we study whether transformer-based language models can extract predicate argument structure from simple sentences. We firstly show that language models sometimes confuse which predicates apply to which objects. To mitigate…
We exploit analogies between first-order algorithms for constrained optimization and non-smooth dynamical systems to design a new class of accelerated first-order algorithms for constrained optimization. Unlike Frank-Wolfe or projected…
Chain-of-Thought (CoT) prompting enables large language models to solve complex reasoning problems by generating intermediate steps. However, confined by its inherent single-pass and sequential generation process, CoT heavily relies on the…
Many reasoning, planning, and problem-solving tasks share an intrinsic algorithmic nature: correctly simulating each step is a sufficient condition to solve them correctly. We collect pairs of naturalistic and synthetic reasoning tasks to…
We address the problem of complementing higher-order patterns without repetitions of existential variables. Differently from the first-order case, the complement of a pattern cannot, in general, be described by a pattern, or even by a…
The task of inferring logical formulas from examples has garnered significant attention as a means to assist engineers in creating formal specifications used in the design, synthesis, and verification of computing systems. Among various…
We prove that, on bounded expansion classes, every first-order formula with modulo counting is equivalent, in a linear-time computable monadic expansion, to an existential first-order formula. As a consequence, we derive, on bounded…
We study the model enumeration problem of the function-free, finite domain fragment of first-order logic with two variables ($FO^2$). Specifically, given an $FO^2$ sentence $\Gamma$ and a positive integer $n$, how can one enumerate all the…
Modern society is full of computational challenges that rely on probabilistic reasoning, statistics, and combinatorics. Interestingly, many of these questions can be formulated by encoding them into propositional formulas and then asking…
This paper is on Bayesian inference for parametric statistical models that are defined by a stochastic simulator which specifies how data is generated. Exact sampling is then possible but evaluating the likelihood function is typically…
Weighted model counting (WMC) is a well-known inference task on knowledge bases, used for probabilistic inference in graphical models. We introduce algebraic model counting (AMC), a generalization of WMC to a semiring structure. We show…
Approximate inference in dynamic systems is the problem of estimating the state of the system given a sequence of actions and partial observations. High precision estimation is fundamental in many applications like diagnosis, natural…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…