Related papers: FO(FD): Extending classical logic with rule-based …
Despite the remarkable performance of Large Language Models (LLMs) in natural language processing tasks, they still struggle with generating logically sound arguments, resulting in potential risks such as spreading misinformation. To…
The most common methods in explainable artificial intelligence are post-hoc techniques which identify the most relevant features used by pretrained opaque models. Some of the most advanced post hoc methods can generate explanations that…
This paper presents an extension of Defeasible Deontic Logic to deal with the Pragmatic Oddity problem. The logic applies three general principles: (1) the Pragmatic Oddity problem must be solved within a general logical treatment of CTD…
We propose a new formalism for specifying and reasoning about problems that involve heterogeneous "pieces of information" -- large collections of data, decision procedures of any kind and complexity and connections between them. The essence…
Local fixpoint iteration describes a technique that restricts fixpoint iteration in function spaces to needed arguments only. It has been studied well for first-order functions in abstract interpretation and also in model checking. Here we…
Uncertainty in Logic Programming has been investigated during the last decades, dealing with various extensions of the classical LP paradigm and different applications. Existing proposals rely on different approaches, such as clause…
Logics for knowledge representation suffer from over-specialization: while each logic may provide an ideal representation formalism for some problems, it is less than optimal for others. A solution to this problem is to choose from several…
We discuss partial specifications in first-order logic FO and also in a Turing-complete extension of FO. We compare the compositional and game-theoretic approaches to the systems.
Logical bilateralism challenges traditional concepts of logic by treating assertion and denial as independent yet opposed acts. While initially devised to justify classical logic, its constructive variants show that both acts admit…
Recently, Baltag and van Benthem arXiv:2103.14946 [cs.LO] introduced a new decidable logic of functional dependence (LFD) with local dependence formulas and dependence quantifiers. The language is interpreted over dependence models, which…
Deep and shallow embeddings of non-classical logics in classical higher-order logic have been explored, implemented, and used in various reasoning tools in recent years. This paper presents a method for the simultaneous deployment of deep…
We consider the family of guarded and unguarded ordered logics, that constitute a recently rediscovered family of decidable fragments of first-order logic (FO), in which the order of quantification of variables coincides with the order in…
The paper describes an extension of well-founded semantics for logic programs with two types of negation. In this extension information about preferences between rules can be expressed in the logical language and derived dynamically. This…
Formalisms based on temporal logics interpreted over finite strict linear orders, known in the literature as finite traces, have been used for temporal specification in automated planning, process modelling, (runtime) verification and…
We seek to find normative criteria of adequacy for nonmonotonic logic similar to the criterion of validity for deductive logic. Rather than stipulating that the conclusion of an inference be true in all models in which the premises are…
Recently, Baltag and van Benthem introduced a decidable logic of functional dependence (LFD) that extends the logic of Cylindrical Relativized Set Algebras (CRS) with atomic local dependence statements. Its semantics can be given in terms…
Interactions between derivatives and fixpoints have many important applications in both computer science and mathematics. In this paper, we provide a categorical framework to combine fixpoints with derivatives by studying Cartesian…
Whether it be in normal form games, or in fair allocations, or in voter preferences in voting systems, a certain pattern of reasoning is common. From a particular profile, an agent or a group of agents may have an incentive to shift to a…
Recursively defined linked data structures embedded in a pointer-based heap and their properties are naturally expressed in pure first-order logic with least fixpoint definitions (FO+lfp) with background theories. Such logics, unlike pure…
How can we reason around logical paradoxes without falling into them? This paper introduces grounded deduction or GD, a Kripke-inspired approach to first-order logic and arithmetic that is neither classical nor intuitionistic, but…