Related papers: Multi-topological semantics for intuitionistic mod…
One of the most common problem-solving heuristics is by analogy. For a given problem, a solver can be viewed as a strategic walk on its fitness landscape. Thus if a solver works for one problem instance, we expect it will also be effective…
Models of complex systems are widely used in the physical and social sciences, and the concept of layering, typically building upon graph-theoretic structure, is a common feature. We describe an intuitionistic substructural logic called…
This work builds upon a well-established research tradition on modal logics of awareness. One of its aims is to export tools and techniques to other areas within modal logic. To this end, we illustrate a number of significant bridges with…
We present a categorical model for intuitionistic linear logic where objects are polynomial diagrams and morphisms are simulation diagrams. The multiplicative structure (tensor product and its adjoint) can be defined in any locally…
This paper combines two studies: a topological semantics for epistemic notions and abstract argumentation theory. In our combined setting, we use a topological semantics to represent the structure of an agent's collection of evidence, and…
Experts do not always feel very, comfortable when they have to give precise numerical estimations of certainty degrees. In this paper we present a qualitative approach which allows for attaching partially ordered symbolic grades to logical…
We introduce the \emph{Arrow Language Model}, a neural architecture derived from an intuitionistic-logic interpretation of next-token prediction. Instead of representing tokens as additive embeddings mixed by attention, we encode a prefix…
Inthispaperwedescribeaconcept-wisemulti-preferencesemantics for description logic which has its root in the preferential approach for modeling defeasible reasoning in knowledge representation. We argue that this proposal, beside satisfying…
A neighborhood graph, which represents the instances as vertices and their relations as weighted edges, is the basis of many semi-supervised and relational models for node labeling and link prediction. Most methods employ a sequential…
This work is a mathematician's attempt to understand intuitionistic logic. It can be read in two ways: as a research paper interspersed with lengthy digressions into rethinking of standard material; or as an elementary (but highly…
This paper addresses the problem of learning the concept of "propagation" in the pretopology theoretical formalism. Our proposal is first to define the pseudo-closure operator (modeling the propagation concept) as a logical combination of…
In systems modelling, a 'system' typically comprises located resources relative to which processes execute. One important use of logic in informatics is in modelling such systems for the purpose of reasoning (perhaps automated) about their…
Iterative abstraction refinement techniques are one of the most prominent paradigms for the analysis and verification of systems with large or infinite state spaces. This paper investigates the changes of truth values of system properties…
The approach taken by Gheorghiu, Gu and Pym in their paper on giving a Base-extension Semantics for Intuitionistic Multiplicative Linear Logic is an interesting adaptation of the work of Sandqvist for IPL to the substructural setting. What…
We propose a novel ranking-based semantics for Dung-style argumentation frameworks with the help of conditional logics. Using an intuitive translation for an argumentation framework to generate conditionals, we can apply nonmonotonic…
Symbolic learning represents the most straightforward approach to interpretable modeling, but its applications have been hampered by a single structural design choice: the adoption of propositional logic as the underlying language.…
Various topological concepts are often involved in the research of mathematical logic, and almost all of these concepts can be regarded as developing from the Stone representation theorem. In the Stone representation theorem, a Boolean…
Recent advances in data-driven models for grounded language understanding have enabled robots to interpret increasingly complex instructions. Two fundamental limitations of these methods are that most require a full model of the environment…
Nonmonotonic logics are usually characterized by the presence of some notion of 'conditional' that fails monotonicity. Research on nonmonotonic logics is therefore largely concerned with the defeasibility of argument forms and the…
We consider the task of learning a context-dependent mapping from utterances to denotations. With only denotations at training time, we must search over a combinatorially large space of logical forms, which is even larger with…