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Answer Set Programming (ASP) is a declarative problem solving paradigm that can be used to encode a combinatorial problem as a logic program whose stable models correspond to the solutions of the considered problem. ASP has been widely…
Logic programming languages present clear advantages in terms of declarativeness and conciseness. However, the ideas of logic programming have been met with resistance in other programming communities, and have not generally been adopted by…
A well-known approach to treating syntactic island constraints in the setting of Lambek grammars consists in adding specific bracket modalities to the logic. We adapt this approach to abstract categorial grammars (ACG). Thus we define…
This extended abstract gives a brief outline of the connections between the descriptions and variable concepts. Thus, the notion of a concept is extended to include both the syntax and semantics features. The evaluation map in use is…
Knowledge can be represented compactly in multiple ways, from a set of propositional formulas, to a Kripke model, to a database. In this paper we study the aggregation of information coming from multiple sources, each source submitting a…
We define a strongly normalising proof-net calculus corresponding to the logic of strongly compact closed categories with biproducts. The calculus is a full and faithful representation of the free strongly compact closed category with…
There has recently been an increasing interest in declarative data analysis, where analytic tasks are specified using a logical language, and their implementation and optimisation are delegated to a general-purpose query engine. Existing…
The emergence of tools based on artificial intelligence has also led to the need of producing explanations which are understandable by a human being. In most approaches, the system is considered a black box, making it difficult to generate…
Large Language Models (LLMs) excel at understanding natural language but struggle with explicit commonsense reasoning. A recent trend of research suggests that the combination of LLM with robust symbolic reasoning systems can overcome this…
Cause-effect relations are an important part of human knowledge. In real life, humans often reason about complex causes linked to complex effects. By comparison, existing formalisms for representing knowledge about causal relations are…
We introduce the relational ontology log, or relational olog, a knowledge representation system based on the category of sets and relations. It is inspired by Spivak and Kent's olog, a recent categorical framework for knowledge…
The paper presents the main characteristics and a preliminary implementation of a novel computational framework named CompLog. Inspired by probabilistic programming systems like ProbLog, CompLog builds upon the inferential mechanisms…
Logics with analogous semantics, such as Fuzzy Logic, have a number of explanatory and application advantages, the most well-known being the ability to help experts develop control systems. From a cognitive systems perspective, such…
In our daily lives and industrial settings, we often encounter dynamic problems that require reasoning over time and metric constraints. These include tasks such as scheduling, routing, and production sequencing. Dynamic logics have…
Visual Question Answering (VQA) is a challenging problem that requires to process multimodal input. Answer-Set Programming (ASP) has shown great potential in this regard to add interpretability and explainability to modular VQA…
Logical relations constitute a key method for reasoning about contextual equivalence of programs in higher-order languages. They are usually developed on a per-case basis, with a new theory required for each variation of the language or of…
We present a formal language with expressions denoting general symbol structures and queries which access information in those structures. A sequence-to-sequence network processing this language learns to encode symbol structures and query…
While in recent years machine learning (ML) based approaches have been the popular approach in developing end-to-end question answering systems, such systems often struggle when additional knowledge is needed to correctly answer the…
Ontology is a popular method for knowledge representation in different domains, including the legal domain, and description logics (DL) is commonly used as its description language. To handle reasoning based on inconsistent DL-based legal…
Solving puzzles in natural language poses a long-standing challenge in AI. While large language models (LLMs) have recently shown impressive capabilities in a variety of tasks, they continue to struggle with complex puzzles that demand…