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Our understanding about things is conceptual. By stating that we reason about objects, it is in fact not the objects but concepts referring to them that we manipulate. Now, so long just as we acknowledge infinitely extending notions such as…
Logical reasoning is central to human cognition and intelligence. It includes deductive, inductive, and abductive reasoning. Past research of logical reasoning within AI uses formal language as knowledge representation and symbolic…
One can find various temporal deontic logics in literature, most focusing on discrete time. The literature on real-time constraints and deontic norms is much sparser. Thus, many analysis techniques which have been developed for deontic…
Modern language models (LMs) exhibit strong deductive reasoning capabilities, yet standard evaluations emphasize correctness while overlooking a key aspect of reasoning: efficiency. In real-world reasoning scenarios, much of the available…
Defeasible logic is an efficient logic for defeasible reasoning. It is defined through a proof theory and, until now, has had no model theory. In this paper a model-theoretic semantics is given for defeasible logic. The logic is sound and…
Formal logic has often been seen as uniquely placed to analyze mathematical argumentation. While formal logic is certainly necessary for a complete understanding of mathematical practice, it is not sufficient. Important aspects of…
Natural language reasoning plays an increasingly important role in improving language models' ability to solve complex language understanding tasks. An interesting use case for reasoning is the resolution of context-dependent ambiguity. But…
This paper investigates formal logics for reasoning about determinacy and independence. Propositional Dependence Logic D and Propositional Independence Logic I are recently developed logical systems, based on team semantics, that provide a…
Adjoint logic is a general approach to combining multiple logics with different structural properties, including linear, affine, strict, and (ordinary) intuitionistic logics, where each proposition has an intrinsic mode of truth. It has…
Nonmonotonic reasoning is a pattern of reasoning that allows an agent to make and retract (tentative) conclusions from inconclusive evidence. This paper gives a possible-worlds interpretation of the nonmonotonic reasoning problem based on…
Recent large language models have demonstrated relevant capabilities in solving problems that require logical reasoning; however, the corresponding internal mechanisms remain largely unexplored. In this paper, we show that a small language…
Transformers have recently been shown to be capable of reliably performing logical reasoning over facts and rules expressed in natural language, but abductive reasoning - inference to the best explanation of an unexpected observation - has…
A semantic tableau method, called an argumentation tableau, that enables the derivation of arguments, is proposed. First, the derivation of arguments for standard propositional and predicate logic is addressed. Next, an extension that…
In this paper a conditional logic is defined and studied. This conditional logic, DmBL, is constructed as close as possible to the Bayesian and is unrestricted, that is one is able to use any operator without restriction. A notion of…
Defeasible logics provide several linguistic features to support the expression of defeasible knowledge. There is also a wide variety of such logics, expressing different intuitions about defeasible reasoning. However, the logics can only…
Higher-level cognition includes logical reasoning and the ability of question answering with common sense. The RatioLog project addresses the problem of rational reasoning in deep question answering by methods from automated deduction and…
We introduce proper display calculi for basic monotonic modal logic,the conditional logic CK and a number of their axiomatic extensions. These calculi are sound, complete, conservative and enjoy cut elimination and subformula property. Our…
Given the large variety of existing logical formalisms it is of utmost importance to select the most adequate one for a specific purpose, e.g. for representing the knowledge relevant for a particular application or for using the formalism…
Inconsistency handling is an important issue in knowledge management. Especially in ontology engineering, logical inconsistencies may occur during ontology construction. A natural way to reason with an inconsistent ontology is to utilize…
Drawing appropriate defeasible inferences has been proven to be one of the most pervasive puzzles of natural language processing and a recurrent problem in pragmatics. This paper provides a theoretical framework, called ``stratified…