Knowledge representation formalisms are aimed to represent general conceptual information and are typically used in the construction of the knowledge base of reasoning agent. A knowledge base can be thought of as representing the beliefs of such an agent. Like a child, a strong-AI (AGI) robot would have to learn through input and experiences, constantly progressing and advancing its abilities over time. Both with statistical AI generated by neural networks we need also the concept of \textsl{causality} of events traduced into directionality of logic entailments and deductions in order to give to robots the emulation of human intelligence. Moreover, by using the axioms we can guarantee the \textsl{controlled security} about robot's actions based on logic inferences. For AGI robots we consider the 4-valued Belnap's bilattice of truth-values with knowledge ordering as well, where the value "unknown" is the bottom value, the sentences with this value are indeed unknown facts, that is, the missed knowledge in the AGI robots. Thus, these unknown facts are not part of the robot's knowledge database, and by learn through input and experiences, the robot's knowledge would be naturally expanded over time. Consequently, this phenomena can be represented by the Closed Knowledge Assumption and Logic Inference provided by this paper. Moreover, the truth-value "inconsistent", which is the top value in the knowledge ordering of Belnap's bilattice, is necessary for strong-AI robots to be able to support such inconsistent information and paradoxes, like Liar paradox, during deduction processes.
Neuro-symbolic AI based on IFOLB is a way to combine neural learning and symbolic reasoning to overcome limitations of purely neural systems (like lack of interpretability and logical structure) with formal logical machinery for self-reference. In this paper we expand the cognitive power of IFOLB by using the probability computation for the currently unknown sentences, based on Nilsson's probability structure for the IFOLB. We introduce the global symmetry transformation that preserves the current knowledge database and logical deduction, and the local one used for real-time decisions about concrete (sub)problems that involve only a very strict subset of IFOLB predicates. The computation of probability density function KI in both cases, based on the Shannon's maximum information entropy, is provided by neural networks of this probabilistic neuro-symbolic AGI.
Given a knowledge base (KB) with a non-entailed fact, the ABox abduction problem asks for possible extensions of the KB that would entail this fact. This problem has many applications, ranging from diagnosis to explainability and repair. ABox abduction has been well-investigated for consistent KBs and classical semantics, but little is known for the case of inconsistent KBs, which can be caused by erroneous data. In this paper we define suitable notions of abduction in this setting and propose criteria that guide abduction towards "useful" hypotheses. To regain meaningful reasoning in the presence of inconsistencies, we use well-established repair semantics. We provide a comprehensive landscape of the complexity of ABox abduction under repair semantics, treating different variants of the abduction problem for the light-weight description logics DL-Lite and EL_bot.
An AI system's output is not the fact or world state it appears to describe, but rather an engineered representation. We propose a semantic framework to describe AI systems, to be able to examine the correctness of such representations. To do so, we distinguish what is justified by accepted domain knowledge, what reference sources say, and what the system can currently use. This allows us to give precise definitions to common failures: extrapolation, refuted or unsupported assertion, sources versus knowledge mismatch, stale or refuted source, added hypotheses, unsupported use... We hope our framework gives a useful vocabulary for specifying and checking AI systems whose outputs, citations, tool calls, and world-changing actions must be justified by reliable claims and explicit authority rather than apparent fluency.