Related papers: Coinductive proof search for polarized logic with …
We present Geometry of Interaction (GoI) models for Multiplicative Polarized Linear Logic, MLLP, which is the multiplicative fragment of Olivier Laurent's Polarized Linear Logic. This is done by uniformly adding multipoints to various…
Pomset logic introduced by Retor\'e is an extension of linear logic with a self-dual noncommutative connective. The logic is defined by means of proof-nets, rather than a sequent calculus. Later a deep inference system BV was developed with…
Legal syllogism is a form of deductive reasoning commonly used by legal professionals to analyze cases. In this paper, we propose legal syllogism prompting (LoT), a simple prompting method to teach large language models (LLMs) for legal…
ACLP is a system which combines abductive reasoning and constraint solving by integrating the frameworks of Abductive Logic Programming (ALP) and Constraint Logic Programming (CLP). It forms a general high-level knowledge representation…
We produce a decidable classical normal modal logic of internalised negation-complete and thus disjunctive non-monotonic interactive proofs (LDiiP) from an existing logical counterpart of non-monotonic or instant interactive proofs (LiiP).…
Recent efforts to improve the reasoning abilities of Large Language Models (LLMs) have focused on integrating formal logic solvers within neurosymbolic frameworks. A key challenge is that formal solvers lack commonsense world knowledge,…
A variety of problems emerged investigating electronic circuits, computer devices and cellular automata motivated a number of attempts to create a differential and integral calculus for Boolean functions. In the present article, we extend…
In sequent calculi, cut elimination is a property that guarantees that any provable formula can be proven analytically. For example, Gentzen's classical and intuitionistic calculi LK and LJ enjoy cut elimination. The property is less…
We advocate here the use of computational logic for systems biology, as a \emph{unified and safe} framework well suited for both modeling the dynamic behaviour of biological systems, expressing properties of them, and verifying these…
We provide a new sequent calculus that enjoys syntactic cut-elimination and strongly terminating backward proof search for the intuitionistic Strong L\"ob logic $\sf{iSL}$, an intuitionistic modal logic with a provability interpretation. A…
Inductive logic programming (ILP) is a form of logical machine learning. The goal is to search a hypothesis space for a hypothesis that generalises training examples and background knowledge. We introduce an approach that 'shrinks' the…
We propose a novel paradigm for solving Inductive Logic Programming (ILP) problems via deep recurrent neural networks. This proposed ILP solver is designed based on differentiable implementation of the deduction via forward chaining. In…
Consider a community of scientists whose labs are each capable of conducting a different set of experiments. The scientists want to work together to confirm a new hypothesis, but to ensure blindness, their labs generally prohibit the…
Temporal logics for hyperproperties have recently emerged as an expressive specification technique for relational properties of reactive systems. While the model checking problem for such logics has been widely studied, there is a scarcity…
Probabilistic Logic Programs (PLPs) generalize traditional logic programs and allow the encoding of models combining logical structure and uncertainty. In PLP, inference is performed by summarizing the possible worlds which entail the query…
This is a short paper about the relationship between logic and computation. More specifically, it is about a relationship between the completeness proof for intuitionistic propositional logic within the form of proof-theoretic semantics…
Nakano's "later" modality, inspired by G\"{o}del-L\"{o}b provability logic, has been applied in type systems and program logics to capture guarded recursion. Birkedal et al modelled this modality via the internal logic of the topos of…
We show that intuitionistic logic is deductively equivalent to Connexive Heyting Logic (CHL), hereby introduced as an example of a strong connexive logic with intuitive semantics. We use the reverse algebraisation paradigm: CHL is presented…
The growing complexity of factual claims in real-world scenarios presents significant challenges for automated fact verification systems, particularly in accurately aggregating and reasoning over multi-hop evidence. Existing approaches…
In this paper we investigate the complexity of abduction, a fundamental and important form of non-monotonic reasoning. Given a knowledge base explaining the world's behavior it aims at finding an explanation for some observed manifestation.…