Related papers: Subsumption in $\mathcal{FL}_{\bot \mathit{reg}}$ …
Defeasible rules are used in providing computable representations of legal documents and, more recently, have been suggested as a basis for explainable AI. Such applications draw attention to the scalability of implementations. The…
Fusions are a simple way of combining logics. For normal modal logics, fusions have been investigated in detail. In particular, it is known that, under certain conditions, decidability transfers from the component logics to their fusion.…
Large language models (LLMs) face significant challenges when processing complex rule systems, as they typically treat interdependent rules as unstructured textual data rather than as logically organized frameworks. This limitation results…
Proving proof-size lower bounds for $\mathbf{LK}$, the sequent calculus for classical propositional logic, remains a major open problem in proof complexity. We shed new light on this challenge by isolating the power of structural rules,…
Separation Logic (SL) with inductive definitions is a natural formalism for specifying complex recursive data structures, used in compositional verification of programs manipulating such structures. The key ingredient of any automated…
In many scenarios, complete and incomplete information coexist. For this reason, the knowledge representation and database communities have long shown interest in simultaneously supporting the closed- and the open-world views when reasoning…
Formal Concept Analysis makes the fundamental observation that any finite lattice $(L, \leq)$ is determined up to isomorphism by the restriction of the relation ${\leq} \subseteq L \times L$ to the set $J(L) \times M(L)$, where $J(L)$ is…
We investigate the computational complexity of the satisfiability problem of modal inclusion logic. We distinguish two variants of the problem: one for the strict and another one for the lax semantics. Both problems turn out to be…
We propose a graph-based extension of Boolean logic called Boolean Graph Logic (BGL). Construing formula trees as the cotrees of cographs, we may state semantic notions such as evaluation and entailment in purely graph-theoretic terms,…
Justification logics are special kinds of modal logics which provide a framework for reasoning about epistemic justifications. For this, they extend classical boolean propositional logic by a family of necessity-style modal operators "t:",…
The formal XAI community has studied a plethora of interpretability queries aiming to understand the classifications made by decision trees. However, a more uniform understanding of what questions we can hope to answer about these models,…
Logic-based approaches to AI have the advantage that their behaviour can in principle be explained by providing their users with proofs for the derived consequences. However, if such proofs get very large, then it may be hard to understand…
The recent series of innovations in deep learning (DL) have shown enormous potential to impact individuals and society, both positively and negatively. The DL models utilizing massive computing power and enormous datasets have significantly…
High-assurance reasoning, particularly in critical domains such as law and medicine, requires conclusions that are accurate, verifiable, and explicitly grounded in evidence. This reasoning relies on premises codified from rules, statutes,…
Interpretability has become a necessary feature for machine learning models deployed in critical scenarios, e.g. legal system, healthcare. In these situations, algorithmic decisions may have (potentially negative) long-lasting effects on…
Both humans and large language models (LLMs) exhibit content effects: biases in which the plausibility of the semantic content of a reasoning problem influences judgments regarding its logical validity. While this phenomenon in humans is…
Traditional neural embeddings represent concepts as points, excelling at similarity but struggling with higher-level reasoning and asymmetric relationships. We introduce a novel paradigm: embedding concepts as linear subspaces. This…
The KLM approach to defeasible reasoning introduces a weakened form of implication into classical logic. This allows one to incorporate exceptions to general rules into a logical system, and for old conclusions to be withdrawn upon learning…
Knowledge bases (KBs) are not static entities: new information constantly appears and some of the previous knowledge becomes obsolete. In order to reflect this evolution of knowledge, KBs should be expanded with the new knowledge and…
We present team semantics for two of the most important linear and branching time specification languages, Linear Temporal Logic (LTL) and Computation Tree Logic (CTL). With team semantics, LTL is able to express hyperproperties, which have…