Related papers: Fuzzy Lattice-based Description Logic
The Lax Logical Framework, LLFP, was introduced, by a team including the last two authors, to provide a conceptual framework for integrating different proof development tools, thus allowing for external evidence and for postponing,…
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…
Rule-based reasoning over natural language input arises in domains where decisions must be auditable and justifiable: clinical protocols specify eligibility criteria in prose, evidence rules define admissibility through textual conditions,…
Many ontologies, i.e., Description Logic (DL) knowledge bases, have been developed to provide rich knowledge about various domains. An ontology consists of an ABox, i.e., assertion axioms between two entities or between a concept and an…
Formal methods are widely recognized as a powerful engineering method for the specification, simulation, development, and verification of distributed interactive systems. However, most formal methods rely on a two-valued logic, and are…
Temporal logics are extensively used for the specification of on-going behaviours of reactive systems. Two significant developments in this area are the extension of traditional temporal logics with modalities that enable the specification…
An approach for encoding abstract dialectical frameworks and their semantics into classical higher-order logic is presented. Important properties and semantic relationships are formally encoded and proven using the proof assistant…
Within the possibilistic approach to uncertainty modeling, the paper presents a modal logical system to reason about qualitative (comparative) statements of the possibility (and necessity) of fuzzy propositions. We relate this qualitative…
We present a KE-tableau-based procedure for the main TBox and ABox reasoning tasks for the description logic $\mathcal{DL}\langle \mathsf{4LQS^{R,\!\times}}\rangle(\mathbf{D})$, in short $\mathcal{DL}_{\mathbf{D}}^{4,\!\times}$. The logic…
Evaluating argument strength in quantitative argumentation systems has received increasing attention in the field of abstract argumentation. The concept of acceptability degree is widely adopted in gradual semantics, however, it may not be…
In this paper we present a theorem proving methodology for a restricted but significant fragment of the conditional language made up of (boolean combinations of) conditional statements with unnested antecedents. The method is based on the…
Many-valued logics in general, and fuzzy logics in particular, usually focus on a notion of consequence based on preservation of full truth, typical represented by the value 1 in the semantics given the real unit interval [0,1]. In a recent…
There has been a growing interest in explaining entailments over description logic (DL) knowledge bases. The existing explanation formalisms focus on justifications to explain true axioms, and abductive reasoning to explain missing axioms…
In-context learning (ICL) has emerged as a successful paradigm for leveraging large language models (LLMs). However, it often struggles to generalize beyond the distribution of the provided demonstrations. A recent advancement in enhancing…
Category theory can be used to state formulas in First-Order Logic without using set membership. Several notable results in logic such as proof of the continuum hypothesis can be elegantly rewritten in category theory. We propose in this…
Among the various forms of reasoning studied in the context of artificial intelligence, qualitative reasoning makes it possible to infer new knowledge in the context of imprecise, incomplete information without numerical values. In this…
This paper analyzes the correctness of the subsumption algorithm used in CLASSIC, a description logic-based knowledge representation system that is being used in practical applications. In order to deal efficiently with individuals in…
We give the first cut-free ExpTime (optimal) tableau decision procedure for checking satisfiability of a knowledge base in the description logic SHI, which extends the description logic ALC with transitive roles, inverse roles and role…
Classical logic has a serious limitation in that it cannot cope with the issues of vagueness and uncertainty into which fall most modes of human reasoning. In order to provide a foundation for human knowledge representation and reasoning in…
The emergence of reasoning-based LLMs leveraging Chain-of-Thought (CoT) inference introduces new serving challenges, as their extended reasoning phases delay user-visible output and inflate Time-To-First-Token (TTFT). Existing LLM serving…