Related papers: Imparo is complete by inverse subsumption

Logical inference algorithms for conditional independence (CI) statements have important applications from testing consistency during knowledge elicitation to constraintbased structure learning of graphical models. We prove that the…

Inference systems are a widespread framework used to define possibly recursive predicates by means of inference rules. They allow both inductive and coinductive interpretations that are fairly well-studied. In this paper, we consider a…

Many forms of inductive logic programming (ILP) use \emph{metarules}, second-order Horn clauses, to define the structure of learnable programs and thus the hypothesis space. Deciding which metarules to use for a given learning task is a…

Tabled evaluation is an implementation technique that solves some problems of traditional Prolog systems in dealing with recursion and redundant computations. Most tabling engines determine if a tabled subgoal will produce or consume…

Reasoning about program correctness has been a central topic in static analysis for many years, with Hoare logic (HL) playing an important role. The key notions in HL are partial and total correctness. Both require that program executions…

In probabilistic reasoning, the traditionally discrete domain has been elevated to the hybrid domain encompassing additionally continuous random variables. Inference in the hybrid domain, however, usually necessitates to condone trade-offs…

We develop a self-learning approach for conjecturing of induction predicates on a dataset of 16197 problems derived from the OEIS. These problems are hard for today's SMT and ATP systems because they require a combination of inductive and…

In this work, we develop a formal system of inductive logic. It uses an infinitary language that allows for countable conjunctions and disjunctions. It is based on a set of nine syntactic rules of inductive inference, and contains classical…

In this paper we describe an algorithm for implicitizing rational hypersurfaces in case there exists at most a finite number of base points. It is based on a technique exposed in math.AG/0210096, where implicit equations are obtained as…

Separation Logic with inductive definitions is a well-known approach for deductive verification of programs that manipulate dynamic data structures. Deciding verification conditions in this context is usually based on user-provided lemmas…

"Induction heads" are attention heads that implement a simple algorithm to complete token sequences like [A][B] ... [A] -> [B]. In this work, we present preliminary and indirect evidence for a hypothesis that induction heads might…

We introduce an inductive logic programming approach that combines classical divide-and-conquer search with modern constraint-driven search. Our anytime approach can learn optimal, recursive, and large programs and supports predicate…

We study the complexity of invariant inference and its connections to exact concept learning. We define a condition on invariants and their geometry, called the fence condition, which permits applying theoretical results from exact concept…

The framework of algorithmic knowledge assumes that agents use algorithms to compute the facts they explicitly know. In many cases of interest, a deductive system, rather than a particular algorithm, captures the formal reasoning used by…

When prompted with a few examples and intermediate steps, large language models (LLMs) have demonstrated impressive performance in various reasoning tasks. However, prompting methods that rely on implicit knowledge in an LLM often generate…

Most successful machine intelligence systems rely on gradient-based learning, which is made possible by backpropagation. Some systems are designed to aid us in interpreting data when explicit goals cannot be provided. These unsupervised…

The emphasis is made on the juxtaposition of (quantum~theorem) proving versus quantum (theorem~proving). The logical contents of verification of the statements concerning quantum systems is outlined. The Zittereingang (trembling input)…

We study a natural variant of the implicational fragment of propositional logic. Its formulas are pairs of conjunctions of positive literals, related together by an implicational-like connective; the semantics of this sort of implication is…

Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. In this paper, we will survey the use of structural proof theory as an alternative foundation. Researchers have been using…

In this note, we show the class of finite, epistemic programs to be Turing complete. Epistemic programs is a widely used update mechanism used in epistemic logic, where it such are a special type of action models: One which does not contain…