Aristotelian diagrams, such as the square of opposition, are well-known in context normal modal logics (i.e., systems logic which can be given a relational semantics terms Kripke models). This paper studies diagrams for non-normal (based on neighborhood semantics, topologically inspired generalization semantics). In particular, we investigate phenomenon logic-sensitivity diagrams. We distinguis...

We suggested in 12] a general logical formalism for Logic Programming based on a four-valued inference. In this paper we give a uniform representation of various semantics for logic programs based on this formalism. The main conclusion from this representation is that the distinction between these semantics can be largely attributed to the diierence in their underlying (monotonic) logical syste...

We propose a proof-theoretical way of obtaining detailed and precise information on conceptual hierarchies. The notion of concept finding proof, which represents a hierarchy of concepts, is introduced based on a substructural logic with mingle and strong negation. Mingle, which is a structural inference rule, is used to represent a process for finding a more general (or specific) concept than s...

Relevant logics provide an alternative to classical implication that is capable of accounting for the relationship between the antecedent and the consequence of a valid implication. Relevant implication is usually explained in terms of information required to assess a proposition. By doing so, relevant implication introduces a number of cognitively relevant aspects in the definition of logical ...

We present a Coq formalization of ultrametric spaces and of ultrametric-enriched categories, up to and including the construction of solutions to recursive domain equations in ultrametric-enriched categories. We then show how to apply this semantic setup for giving semantics to a programming language with higher-order store. Specifically, we define a step counting operational semantics for a fu...

A significant part of current research on (inductive) logic programming deals with probabilistic logical models. Over the last decade many logics or languages for representing such models have been introduced. There is currently a great need for insight into the relationships between all these languages. One kind of languages are those that extend probabilistic models with elements of logic, su...

The semantics of a proof language relies on the representation of the state of a proof after a logical rule has been applied. This information, which is usually meaningless from a logical point of view, is fundamental to describe the control mechanism of the proof search provided by the language. In this paper, we present a monadic datatype to represent the state information of a proof and we i...

Traditional epistemic logic assumes that agents’ knowledge is closed under logical consequence. Many attempts to solve this logical omniscience problem weaken the closure condition by assuming that agents are ignorant of certain logical rules. Duc (1997) avoids the apparent paradox of nonomniscience and non-ignorance by introducing propositions on the form “φ is true after some train of thought...

Distributional semantics focuses on the automatic construction of a semantic model based on the statistical distribution of colocated words in large-scale texts. Deductive reasoning is a fundamental component for semantic understanding. Despite the generality and expressivity of logical models, from an applied perspective, deductive reasoners are dependent on highly consistent conceptual models...

Among the many possible approaches to dealing with logical omniscience, I consider here awareness and impossible worlds structures. The former approach, pioneered by Fagin and Halpern, distinguishes between implicit and explicit knowledge, and avoids logical omniscience with respect to explicit knowledge. The latter, developed by Rantala and by Hintikka, allows for the existence of logically im...