Related papers: Predicate Transformers and Linear Logic, yet anoth…
Linear Logic refines Intuitionnistic Logic by taking into account the resources used during the proof and program computation. In the past decades, it has been extended to various frameworks. The most famous are indexed linear logics which…
Refinement types sharpen systems of simple and dependent types by offering expressive means to more precisely classify well-typed terms. We present a system of refinement types for LF in the style of recent formulations where only canonical…
The paper describes an extension of well-founded semantics for logic programs with two types of negation. In this extension information about preferences between rules can be expressed in the logical language and derived dynamically. This…
We describe an approach for compiling preferences into logic programs under the answer set semantics. An ordered logic program is an extended logic program in which rules are named by unique terms, and in which preferences among rules are…
We present a systematic approach to logical predicates based on universal coalgebra and higher-order abstract GSOS, thus making a first step towards a unifying theory of logical relations. We first observe that logical predicates are…
In this paper, we address the problem of giving names to predicates in logic rules using Large Language Models (LLMs). In the context of Inductive Logic Programming, various rule generation methods produce rules containing unnamed…
Session types capture precise protocol structure in concurrent programming, but do not specify properties of the exchanged values beyond their basic type. Refinement types are a form of dependent types that can address this limitation,…
Recent developments in termination analysis for declarative programs emphasize the use of appropriate models for the logical theory representing the program at stake as a generic approach to prove termination of declarative programs. In…
Recently, symbolic structures were proposed as finite representations of potentially infinite first-order structures, where Linear Integer Arithmetic terms and formulas define the domain and interpretations of a structure. We generalize…
This paper introduces a differentiable semantic reasoner, where rules are presented as a relevant set of graph transformations. These rules can be written manually or inferred by a set of facts and goals presented as a training set. While…
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…
An important characteristic of many logics for Artificial Intelligence is their nonmonotonicity. This means that adding a formula to the premises can invalidate some of the consequences. There may, however, exist formulae that can always be…
Processing programs as data is one of the successes of functional and logic programming. Higher-order functions, as program-processing programs are called in functional programming, and meta-programs, as they are called in logic…
One way to interpret the reasoning power of transformer-based language models is to describe the types of logical rules they can resolve over some input text. Recently, Chiang et al. (2023) showed that finite-precision transformers can be…
Temporal logic is a framework for representing and reasoning about propositions that evolve over time. It is commonly used for specifying requirements in various domains, including hardware and software systems, as well as robotics.…
We present a domain-specific type theory for constructions and proofs in category theory. The type theory axiomatizes notions of category, functor, profunctor and a generalized form of natural transformations. The type theory imposes an…
A semantic model enjoys full definability if every semantic element in the model is a denotation of some proof or program. Full definability indicates that the model captures programs and proofs in a highly detailed manner. This paper…
When predictive models are used to support complex and important decisions, the ability to explain a model's reasoning can increase trust, expose hidden biases, and reduce vulnerability to adversarial attacks. However, attempts at…
Many applications of denotational semantics, such as higher-order model checking or the complexity of normalization, rely on finite semantics for monomorphic type systems. We exhibit such a finite semantics for a polymorphic purely linear…
We consider an extension of logic programs, called \omega-programs, that can be used to define predicates over infinite lists. \omega-programs allow us to specify properties of the infinite behavior of reactive systems and, in general,…