Related papers: A Logic for Paraconsistent Transition Systems
Often in Software Engineering, a modeling formalism has to support scenarios of inconsistency in which several requirements either reinforce or contradict each other. Paraconsistent transition systems are proposed in this paper as one such…
Transition systems are often used to describe the behaviour of software systems. If viewed as a graph then, at their most basic level, vertices correspond to the states of a program and each edge represents a transition between states via…
Multi-Context Systems are an expressive formalism to model (possibly) non-monotonic information exchange between heterogeneous knowledge bases. Such information exchange, however, often comes with unforseen side-effects leading to violation…
Classical logic predicts that everything (thus nothing useful at all) follows from inconsistency. A paraconsistent logic is a logic where an inconsistency does not lead to such an explosion, and since in practice consistency is difficult to…
For a newcomer, paraconsistent logics can be difficult to grasp. Even experts in logic can find the concept of paraconsistency to be suspicious or misguided, if not actually wrong. The problem is that although they usually have much in…
It is argued that 4-valued paraconsistent truth values (called here "p-bits") can serve as a conceptual, mathematical and practical foundation for highly AI-relevant forms of probabilistic logic and probabilistic programming and concept…
We describe a method to axiomatize computations in deterministic Turing machines. When applied to computations in non-deterministic Turing machines, this method may produce contradictory (and therefore trivial) theories, considering…
Data consistency is very desirable because strong semantic properties make it easier to write correct programs that perform as users expect. However, there are good reasons why consistency may have to be weakened to achieve other business…
We explore the problem of explaining observations starting from a classically inconsistent theory by adopting a paraconsistent framework. We consider two expansions of the well-known Belnap--Dunn paraconsistent four-valued logic…
A thorough investigation of the foundations of paraconsistent logics. Relations between logical principles are formally studied, a novel notion of consistency is introduced, the logics of formal inconsistency, and the subclasses of…
One advantage of paraconsistent logic is that it can deal with inconsistencies without making the system trivial. However, unlike classical propositional calculus, its deductive system is limited, and the meaning of paraconsistent negation…
We propose a way of reasoning about minimal and maximal values of the weights of transitions in a weighted transition system (WTS). This perspective induces a notion of bisimulation that is coarser than the classic bisimulation: it relates…
There currently exists a gap between the theories proposed by the probability and uncertainty and the needs of Artificial Intelligence research. These theories primarily address the needs of expert systems, using knowledge structures which…
Inverse problems arise in situations where data is available, but the underlying model is not. It can therefore be necessary to infer the parameters of the latter starting from the former. Statistical mechanics offers a toolbox of…
Superstatistics is a widely employed tool of non-equilibrium statistical physics which plays an important role in analysis of hierarchical complex dynamical systems. Yet, its "canonical" formulation in terms of a single nuisance parameter…
Belnap-Dunn's relevance logic, BD, was designed seeking a suitable logical device for dealing with multiple information sources which sometimes may provide inconsistent and/or incomplete pieces of information. BD is a four-valued logic…
The goal of computational logic is to allow us to model computation as well as to reason about it. We argue that a computational logic must be able to model interactive computation. We show that first-order logic cannot model interactive…
It is argued that a fuzzy version of 4-truth-valued paraconsistent logic (with truth values corresponding to True, False, Both and Neither) can be approximately isomorphically mapped into the complex-number algebra of quantum probabilities.…
We present a novel approach to querying classical inconsistent description logic (DL) knowledge bases by adopting a~paraconsistent semantics with the four Belnapian values: exactly true ($\mathbf{T}$), exactly false ($\mathbf{F}$), both…
The study of intelligent systems explains behaviour in terms of economic rationality. This results in an optimization principle involving a function or utility, which states that the system will evolve until the configuration of maximum…