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This paper presents a Prolog-based reasoning module to generate counterfactual explanations given the predictions computed by a black-box classifier. The proposed symbolic reasoning module can also resolve what-if queries using the…
Building rules on top of ontologies is the ultimate goal of the logical layer of the Semantic Web. To this aim an ad-hoc mark-up language for this layer is currently under discussion. It is intended to follow the tradition of hybrid…
The logical semantics of normal logic programs has traditionally been based on the notions of Clark's completion and two-valued or three-valued canonical models, including supported, stable, regular, and well-founded models. Two-valued…
Differentiable logics are a family of quantitative logics originated in the machine learning literature. Because of their origin, differentiable logics often come equipped with analytic properties that guarantee that they are…
Fuzzy Description Logics (FDLs) are logic-based formalisms used to represent and reason with vague or imprecise knowledge. It has been recently shown that reasoning in most FDLs using truth values from the interval [0,1] becomes undecidable…
Fuzzy reasoning is a very productive research field that during the last years has provided a number of theoretical approaches and practical implementation prototypes. Nevertheless, the classical implementations, like Fril, are not adapted…
We propose a combination of probabilistic reasoning from conditional constraints with approaches to default reasoning from conditional knowledge bases. In detail, we generalize the notions of Pearl's entailment in system Z, Lehmann's…
We propose a purely extensional semantics for higher-order logic programming. In this semantics program predicates denote sets of ordered tuples, and two predicates are equal iff they are equal as sets. Moreover, every program has a unique…
Processing long contexts is increasingly important for Large Language Models (LLMs) in tasks like multi-turn dialogues, code generation, and document summarization. This paper addresses the challenges of achieving high long-context…
The modal systems S1--S3 were introduced by C. I. Lewis as logics for strict implication. While there are Kripke semantics for S2 and S3, there is no known natural semantics for S1. We extend S1 by a Substitution Principle SP which…
Classical logic has a serious limitation in that it cannot cope with the issues of vagueness and uncertainty into which fall most modes of human reasoning. In order to provide a foundation for human knowledge representation and reasoning in…
Lambda Prolog is known to be well-suited for expressing and implementing logics and inference systems. We show that lemmas and definitions in such logics can be implemented with a great economy of expression. We encode a higher-order logic…
Logical frameworks based on intuitionistic or linear logics with higher-type quantification have been successfully used to give high-level, modular, and formal specifications of many important judgments in the area of programming languages…
Modern applications combine information from a great variety of sources. Oftentimes, some of these sources, like Machine-Learning systems, are not strictly binary but associated with some degree of (lack of) confidence in the observation.…
We introduce two-dimensional logics based on \L{}ukasiewicz and G\"{o}del logics to formalize paraconsistent fuzzy reasoning. The logics are interpreted on matrices, where the common underlying structure is the bi-lattice (twisted) product…
Logic programming has developed as a rich field, built over a logical substratum whose main constituent is a nonclassical form of negation, sometimes coexisting with classical negation. The field has seen the advent of a number of…
The study of representations is of fundamental importance to any form of communication, and our ability to exploit them effectively is paramount. This article presents a novel theory -- Representational Systems Theory -- that is designed to…
Logic $L$ was introduced by Lewitzka [7] as a modal system that combines intuitionistic and classical logic: $L$ is a conservative extension of CPC and it contains a copy of IPC via the embedding $\varphi\mapsto\square\varphi$. In this…
Many-valued logics in general, and fuzzy logics in particular, usually focus on a notion of consequence based on preservation of full truth, typical represented by the value 1 in the semantics given the real unit interval [0,1]. In a recent…
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…