Related papers: PUC-Logic embedding of Lewis' Deontic Logics
For performance and verification in machine learning, new methods have recently been proposed that optimise learning systems to satisfy formally expressed logical properties. Among these methods, differentiable logics (DLs) are used to…
We present a propositional logic %which can be used to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and…
We extend the {\lambda}-calculus with constructs suitable for relational and functional-logic programming: non-deterministic choice, fresh variable introduction, and unification of expressions. In order to be able to unify…
This paper develops a declarative language, P-log, that combines logical and probabilistic arguments in its reasoning. Answer Set Prolog is used as the logical foundation, while causal Bayes nets serve as a probabilistic foundation. We give…
We prove strong completeness results for some modal logics with the universal modality, with respect to their topological semantics over 0-dimensional dense-in-themselves metric spaces. We also use failure of compactness to show that, for…
We present a linearity theorem for a proof language of intuitionistic multiplicative additive linear logic, incorporating addition and scalar multiplication. The proofs in this language are linear in the algebraic sense. This work is part…
While the recent Chain-of-Thought (CoT) technique enhances the reasoning ability of large language models (LLMs) with the theory of mind, it might still struggle in handling logical reasoning that relies much on symbolic expressions and…
Logical frameworks can be used to translate proofs from a proof system to another one. For this purpose, we should be able to encode the theory of the proof system in the logical framework. The Lambda Pi calculus modulo theory is one of…
Large vision-language models (LVLMs) have demonstrated remarkable capabilities by integrating pre-trained vision encoders with large language models (LLMs). Similar to single-modal LLMs, chain-of-thought (CoT) prompting has been adapted for…
We present a simple resolution proof system for higher-order constrained Horn clauses (HoCHC) - a system of higher-order logic modulo theories - and prove its soundness and refutational completeness w.r.t. the standard semantics. As…
We present Bicoq3, a deep embedding of the B system in Coq, focusing on the technical aspects of the development. The main subjects discussed are related to the representation of sets and maps, the use of induction principles, and the…
We develop a classical propositional logic for reasoning about combinatory logic. We define its syntax, axiomatic system and semantics. The syntax and axiomatic system are presented based on classical propositional logic, with typed…
A new syntactic characterization of problems complete via Turing reductions is presented. General canonical forms are developed in order to define such problems. One of these forms allows us to define complete problems on ordered…
We obtain poly-time embeddings of the intuitionistic modal logics FS and MIPC into their positive one-variable fragments.
This paper presents a new system of logic, LF, that is intended to be used as the foundation of the formalization of science. That is, deductive validity according to LF is to be used as the criterion for assessing what follows from the…
The formalization of action and obligation using logic languages is a topic of increasing relevance in the field of ethics for AI. Having an expressive syntactic and semantic framework to reason about agents' decisions in moral situations…
Defeasible logic is a rule-based nonmonotonic logic, with both strict and defeasible rules, and a priority relation on rules. We show that inference in the propositional form of the logic can be performed in linear time. This contrasts…
The paper gives a soundness and completeness proof for the implicative fragment of intuitionistic calculus with respect to the semantics of computability logic, which understands intuitionistic implication as interactive algorithmic…
Recursive definitions of predicates are usually interpreted either inductively or coinductively. Recently, a more powerful approach has been proposed, called flexible coinduction, to express a variety of intermediate interpretations,…
In this paper we investigate further the tableaux system for a deontic action logic we presented in previous work. This tableaux system uses atoms (of a given boolean algebra of action terms) as labels of formulae, this allows us to embrace…