Related papers: Automated Mutual Explicit Induction Proof in Separ…
We introduce a new logic that combines Adjoint Logic with Graded Necessity Modalities. This results in a very expressive system capable of controlling when and how structural rules are used. We give a sequent calculus, natural deduction,…
We formulate a framework for describing behaviour of effectful higher-order recursive programs. Examples of effects are implemented using effect operations, and include: execution cost, nondeterminism, global store and interaction with a…
Answering complex questions that require making latent decisions is a challenging task, especially when limited supervision is available. Recent works leverage the capabilities of large language models (LMs) to perform complex question…
We introduce DeepProbLog, a probabilistic logic programming language that incorporates deep learning by means of neural predicates. We show how existing inference and learning techniques can be adapted for the new language. Our experiments…
We study and derive algorithms for nonlinear eigenvalue problems, where the system matrix depends on the eigenvector, or several eigenvectors (or their corresponding invariant subspace). The algorithms are derived from an implicit…
We present a static analysis technique for non-termination inference of logic programs. Our framework relies on an extension of the subsumption test, where some specific argument positions can be instantiated while others are generalized.…
Automatically proving separation logic entailments is a fundamental challenge in verification. While rule-based methods rely on separation logic rules (lemmas) for automation, these rule statements are insufficient for describing automation…
We extend Natural Deduction for intuitionistic logic with a third introduction rule for the disjunction, $\vee$-i3, with a conclusion $\Gamma\vdash A\vee B$, but both premises $\Gamma\vdash A$ and $\Gamma\vdash B$. This rule is admissible…
First-order logic (FOL) can represent the logical entailment semantics of natural language (NL) sentences, but determining natural language entailment using FOL remains a challenge. To address this, we propose the Entailment-Preserving FOL…
I show that propositional intuitionistic logic is complete with respect to an adaptation of Dummett's pragmatist justification procedure. In particular, given a pragmatist justification of an argument, I show how to obtain a natural…
Transition Algebra (TA) is a type of infinite logic introduced to discuss rewriting systems. The natural deductive proof systems already introduced in TA satisfy completeness for countable signatures. However, it lacks compactness, making…
Logic-based approaches to AI have the advantage that their behavior can in principle be explained to a user. If, for instance, a Description Logic reasoner derives a consequence that triggers some action of the overall system, then one can…
The goal of this paper is to extend classical logic with a generalized notion of inductive definition supporting positive and negative induction, to investigate the properties of this logic, its relationships to other logics in the area of…
We introduce proper display calculi for intuitionistic, bi-intuitionistic and classical linear logics with exponentials, which are sound, complete, conservative, and enjoy cut-elimination and subformula property. Based on the same design,…
Mathematical proof aims to deliver confident conclusions, but a very similar process of deduction can be used to make uncertain estimates that are open to revision. A key ingredient in such reasoning is the use of a "default" estimate of…
The purpose of this paper is to develop and study recursive proofs of coinductive predicates. Such recursive proofs allow one to discover proof goals in the construction of a proof of a coinductive predicate, while still allowing the use of…
We define a fragment of monadic infinitary second-order logic corresponding to an abstract separation property. We use this to define the concept of a separation subclass. We use model theoretic techniques and games to show that separation…
We consider the problem of intruder deduction in security protocol analysis: that is, deciding whether a given message $M$ can be deduced from a set of messages $\Gamma$ under the theory of blind signatures and arbitrary convergent…
Full Intuitionistic Linear Logic (FILL) is multiplicative intuitionistic linear logic extended with par. Its proof theory has been notoriously difficult to get right, and existing sequent calculi all involve inference rules with complex…
This article contains a proposal to add coinduction to the computational apparatus of natural language understanding. This, we argue, will provide a basis for more realistic, computationally sound, and scalable models of natural language…