Related papers: On Rational Closure in Description Logics of Typic…
Definite descriptions, such as 'the smallest planet in the Solar System', have been recently recognised as semantically transparent devices for object identification in knowledge representation formalisms. Along with individual names, they…
We define a family of intuitionistic non-normal modal logics; they can bee seen as intuitionistic counterparts of classical ones. We first consider monomodal logics, which contain only one between Necessity and Possibility. We then consider…
We study transformational program logics for correctness and incorrectness that we extend to explicitly handle both termination and nontermination. We show that the logics are abstract interpretations of the right image transformer for a…
With the rise of knowledge management and knowledge economy, the knowledge elements that directly link and embody the knowledge system have become the research focus and hotspot in certain areas. The existing knowledge element…
Most modern formalisms used in Databases and Artificial Intelligence for describing an application domain are based on the notions of class (or concept) and relationship among classes. One interesting feature of such formalisms is the…
For those of us who generally live in the world of syntax, semantic proof techniques such as reducibility, realizability or logical relations seem somewhat magical despite -- or perhaps due to -- their seemingly unreasonable effectiveness.…
We introduce proper display calculi for intuitionistic, bi-intuitionistic and classical linear logics with exponentials, which are sound, complete, conservative, and enjoy cut-elimination and subformula property. Based on the same design,…
Logic-based approaches to AI have the advantage that their behavior can in principle be explained to a user. If, for instance, a Description Logic reasoner derives a consequence that triggers some action of the overall system, then one can…
On one hand, termination analysis of logic programs is now a fairly established research topic within the logic programming community. On the other hand, non-termination analysis seems to remain a much less attractive subject. If we divide…
We extend the {\lambda}-calculus with constructs suitable for relational and functional-logic programming: non-deterministic choice, fresh variable introduction, and unification of expressions. In order to be able to unify…
Recently, arXiv:2312.16035 showed that all logics based on Boolean Normal monotonic three-valued schemes coincide with classical logic when defined using a strict-tolerant standard ($\mathbf{st}$). Conversely, they proved that under a…
We present a new approach to termination analysis of logic programs. The essence of the approach is that we make use of general term-orderings (instead of level mappings), like it is done in transformational approaches to logic program…
In this paper we develop a concept aware multi-preferential semantics for dealing with typicality in description logics, where preferences are associated with concepts, starting from a collection of ranked TBoxes containing defeasible…
Modal logic is a paradigm for several useful and applicable formal systems in computer science. It generally retains the low complexity of classical propositional logic, but notable exceptions exist in the domains of description, temporal,…
Temporal reasoning with conditionals is more complex than both classical temporal reasoning and reasoning with timeless conditionals, and can lead to some rather counter-intuitive conclusions. For instance, Aristotle's famous "Sea Battle…
The study of finite automata and regular languages is a privileged meeting point of algebra and logic. Since the work of Buchi, regular languages have been classified according to their descriptive complexity, i.e. the type of logical…
We give the first ExpTime (complexity-optimal) tableau decision procedure for checking satisfiability of a knowledge base in the description logic SHOQ, which extends the basic description logic ALC with transitive roles, hierarchies of…
We define a strongly normalising proof-net calculus corresponding to the logic of strongly compact closed categories with biproducts. The calculus is a full and faithful representation of the free strongly compact closed category with…
This paper proposes a new approach to defining and expressing algorithms: the notion of {\it task logical} algorithms. This notion allows the user to define an algorithm for a task $T$ as a set of agents who can collectively perform $T$.…
Neural rationale models are popular for interpretable predictions of NLP tasks. In these, a selector extracts segments of the input text, called rationales, and passes these segments to a classifier for prediction. Since the rationale is…