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We introduce a novel, logic-independent framework for the study of sequent-style proof systems, which covers a number of proof-theoretic formalisms and concrete proof systems that appear in the literature. In particular, we introduce a…
In relatively free word order languages, grammatical functions are intricately related to case marking. Assuming an ordered representation of the predicate-argument structure, this work proposes a Combinatory Categorial Grammar formulation…
This paper presents matching logic, a first-order logic (FOL) variant for specifying and reasoning about structure by means of patterns and pattern matching. Its sentences, the patterns, are constructed using variables, symbols, connectives…
Foundational verification considers the functional correctness of programming languages with formalized semantics and uses proof assistants (e.g., Coq, Isabelle) to certify proofs. The need for verifying complex programs compels it to…
Sharing of notations and theories across an inheritance hierarchy of mathematical structures, e.g., groups and rings, is important for productivity when formalizing mathematics in proof assistants. The packed classes methodology is a…
We propose a formal treatment of scenarios in the context of a dialectical argumentation formalism for qualitative reasoning about uncertain propositions. Our formalism extends prior work in which arguments for and against uncertain…
Inferring from inconsistency and making decisions are two problems which have always been treated separately by researchers in Artificial Intelligence. Consequently, different models have been proposed for each category. Different…
In quantum information and computation research, symbolic methods have been widely used for human specification and reasoning about quantum states and operations. At the same time, they are essential for ensuring the scalability and…
There is a growing need for abstractions in logic specification languages such as FO(.) and ASP. One technique to achieve these abstractions are templates (sometimes called macros). While the semantics of templates are virtually always…
This work establishes a robust mathematical foundation for compositional System Dynamics modeling, leveraging category theory to formalize and enhance the representation, analysis, and composition of system models. Here, System Dynamics…
Classical planning representation languages based on first-order logic have preliminarily been used to model and solve robotic task planning problems. Wider adoption of these representation languages, however, is hindered by the limitations…
The logical parallelism of propositional connectives and type constructors extends beyond the static realm of predicates, to the dynamic realm of processes. Understanding the logical parallelism of process propositions and dynamic types was…
Argumentation is a very active research field of Artificial Intelligence concerned with the representation and evaluation of arguments used in dialogues between humans and/or artificial agents. Acceptability semantics of formal…
This the first of a series of articles dealing with abstract classification theory. The apparatus to assign systems of cardinal invariants to models of a first order theory (or determine its impossibility) is developed in [Sh:a]. It is…
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…
In this paper, we propose a set theoretic approach for knowledge representation. While the syntax of an application domain is captured by set theoretic constructs including individuals, concepts and operators, knowledge is formalized by…
New Foundations ($\mathrm{NF}$) is a set theory obtained from naive set theory by putting a stratification constraint on the comprehension schema; for example, it proves that there is a universal set $V$. $\mathrm{NFU}$ ($\mathrm{NF}$ with…
In this article, we present a novel approach for parsing argumentation structures. We identify argument components using sequence labeling at the token level and apply a new joint model for detecting argumentation structures. The proposed…
We investigate the decidability of the definability problem for fragments of first order logic over finite words enriched with modular predicates. Our approach aims toward the most generic statements that we could achieve, which…
The paper introduces a novel framework based on category theory to enhance the explainability of artificial intelligence systems, particularly focusing on word embeddings. Key topics include the construction of categories $\mathcal{L}_T$…