Related papers: The Forms of Categorical Proposition
The present paper addresses several puzzles related to the Rule of Existential Generalization, (EG). In solution to these puzzles from the viewpoint of simple type theory, I distinguish (EG) from a modified Rule of Existential Quantifier…
In this paper we discuss contrastive explanations for formal argumentation - the question why a certain argument (the fact) can be accepted, whilst another argument (the foil) cannot be accepted under various extension-based semantics. The…
Argumentation theory is a powerful paradigm that formalizes a type of commonsense reasoning that aims to simulate the human ability to resolve a specific problem in an intelligent manner. A classical argumentation process takes into account…
Despite recent advances in automating theorem proving in full first-order theories, inductive reasoning still poses a serious challenge to state-of-the-art theorem provers. The reason for that is that in first-order logic induction requires…
Many representation schemes combining first-order logic and probability have been proposed in recent years. Progress in unifying logical and probabilistic inference has been slower. Existing methods are mainly variants of lifted variable…
This paper defines the (first-order) conflict resolution calculus: an extension of the resolution calculus inspired by techniques used in modern SAT-solvers. The resolution inference is restricted to (first-order) unit-propagation and the…
This paper studies a fundamental mechanism of how to detect a conflict between arguments given sentiments regarding acceptability of the arguments. We introduce a concept of the inverse problem of the abstract argumentation to tackle the…
We study first-order logic over unordered structures whose elements carry a finite number of data values from an infinite domain which can be compared wrt. equality. As the satisfiability problem for this logic is undecidable in general, in…
This paper relates the well-known Linear Temporal Logic with the logic of propositional schemata introduced by the authors. We prove that LTL is equivalent to a class of schemata in the sense that polynomial-time reductions exist from one…
Applying logic in the area of conceptual modeling has been investigated widely, yet there has been limited uptake of logic-based conceptual modeling in industry. According to some researchers, another formalization of such tools as EER or…
Qualitative reasoning involves expressing and deriving knowledge based on qualitative terms such as natural language expressions, rather than strict mathematical quantities. Well over 40 qualitative calculi have been proposed so far, mostly…
We consider a general statistical linear inverse problem, where the solution is represented via a known (possibly overcomplete) dictionary that allows its sparse representation. We propose two different approaches. A model selection…
We consider the question of extending propositional logic to a logic of plausible reasoning, and posit four requirements that any such extension should satisfy. Each is a requirement that some property of classical propositional logic be…
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 classical satisfiability problem (SAT) is used as a natural and general tool to express and solve combinatorial problems that are in NP. We postulate that provability for implicational intuitionistic propositional logic (IIPC) can serve…
Logically constrained term rewriting is a rewriting framework that supports built-in data structures such as integers and bit vectors. Recently, constrained terms play a key role in various analyses and applications of logically constrained…
This paper provides two extensions of first order logic by `$\omega$-rules'. In each case we characterize the countable structures whose theory in the logic is categorical (has a unique model). In the one-sorted inferential $\omega$-logic,…
There is a generic way to add any new feature to a system. It involves 1) identifying the basic units which build up the system and 2) introducing the new feature to each of these basic units. In the case where the system is argumentation…
Formal verification via theorem proving enables the expressive specification and rigorous proof of software correctness, but it is difficult to scale due to the significant manual effort and expertise required. While Large Language Models…
We study the complexity of the model checking problem, for fixed model A, over certain fragments L of first-order logic. These are sometimes known as the expression complexities of L. We obtain various complexity classification theorems for…