Related papers: Inductive Reasoning with Equality Predicates, Cont…

The usual reading of logical implication "A implies B" as "if A then B" fails in intuitionistic logic: there are formulas A and B such that "A implies B" is not provable, even though B is provable whenever A is provable. Intuitionistic…

We present automated theorem provers for the first-order logic of here and there (HT). They are based on a native sequent calculus for the logic of HT and an axiomatic embedding of the logic of HT into intuitionistic logic. The analytic…

Traditional automated theorem provers for first-order logic depend on speed-optimized search and many handcrafted heuristics that are designed to work best over a wide range of domains. Machine learning approaches in literature either…

In the theory of programming languages, type inference is the process of inferring the type of an expression automatically, often making use of information from the context in which the expression appears. Such mechanisms turn out to be…

We consider the problem of automated reasoning about dynamically manipulated data structures. The state-of-the-art methods are limited to the unfold-and-match (U+M) paradigm, where predicates are transformed via (un)folding operations…

Given a conditional sentence "P=>Q" (if P then Q) and respective facts, four different types of inferences are observed in human reasoning. Affirming the antecedent (AA) (or modus ponens) reasons Q from P; affirming the consequent (AC)…

We consider an extension of bi-intuitionistic logic with the traditional modalities from tense logic Kt. Proof theoretically, this extension is obtained simply by extending an existing sequent calculus for bi-intuitionistic logic with…

We present two algorithms for exact and approximate inference in causal networks. The first algorithm, dynamic conditioning, is a refinement of cutset conditioning that has linear complexity on some networks for which cutset conditioning is…

In learning-assisted theorem proving, one of the most critical challenges is to generalize to theorems unlike those seen at training time. In this paper, we introduce INT, an INequality Theorem proving benchmark, specifically designed to…

Text infilling is defined as a task for filling in the missing part of a sentence or paragraph, which is suitable for many real-world natural language generation scenarios. However, given a well-trained sequential generative model,…

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…

In this position paper, we propose a reasoning framework that can model the reasoning process underlying natural language inferences. The framework is based on the semantic tableau method, a well-studied proof system in formal logic. Like…

In previous work [Lewitzka, Log. J. IGPL 2017], we presented a hierarchy of classical modal systems, along with algebraic semantics, for the reasoning about intuitionistic truth, belief and knowledge. Deviating from G\"odel's interpretation…

In introductory books about natural numbers, a common kind of assertion - often left as exercise to the reader - is that certain forms of induction on $\mathbb{N}$ (regular/ordinary, complete/strong) are equivalent one to each other and to…

Formally verifying the correctness of mathematical proofs is more accessible than ever, however, the learning curve remains steep for many of the state-of-the-art interactive theorem provers (ITP). Deriving the most appropriate subsequent…

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…

Multiplicative linear logic is a very well studied formal system, and most such studies are concerned with the one-sided sequent calculus. In this paper we look in detail at existing translations between a deep inference system and the…

Human reasoning can often be understood as an interplay between two systems: the intuitive and associative ("System 1") and the deliberative and logical ("System 2"). Neural sequence models -- which have been increasingly successful at…

With the advancement of large language models (LLMs), solving complex reasoning tasks has gained increasing attention. Inference-time computation methods (e.g., Best-of-N, beam search, et al.) are particularly valuable as they can enhance…

Prediction without justification has limited applicability. As a remedy, we learn to extract pieces of input text as justifications -- rationales -- that are tailored to be short and coherent, yet sufficient for making the same prediction.…