Related papers: {\L}ukasiewicz mu-Calculus
We study a real valued propositional logic with unbounded positive and negative truth values that we call R-valued logic. Such logic slightly extends continuous propositional logic which, in turn, builds on Lukasiewicz many-valued logic.…
Metric Temporal Logic $\mathsf{MTL}[\until_I,\since_I]$ is one of the most studied real time logics. It exhibits considerable diversity in expressiveness and decidability properties based on the permitted set of modalities and the nature of…
We present a fuzzy (or quantitative) version of the van Benthem theorem, which characterizes propositional modal logic as the bisimulation-invariant fragment of first-order logic. Specifically, we consider a first-order fuzzy predicate…
We introduce $\textit{PCFTL (Probabilistic CounterFactual Temporal Logic)}$, a new probabilistic temporal logic for the verification of Markov Decision Processes (MDP). PCFTL is the first to include operators for causal reasoning, allowing…
Temporal logics over finite traces have recently seen wide application in a number of areas, from business process modelling, monitoring, and mining to planning and decision making. However, real-life dynamic systems contain a degree of…
This paper surveys main and recent studies on temporal logics in a broad sense by presenting various logic systems, dealing with various time structures, and discussing important features, such as decidability (or undecidability) results,…
The probability theory is a well-studied branch of mathematics, in order to carry out formal reasoning about probability. Thus, it is important to have a logic, both for computation of probabilities and for reasoning about probabilities,…
In this paper, we generalize modal $\mu$-calculus to the non-distributive (lattice-based) modal $\mu$-calculus and formalize some scenarios regarding categorization using it. We also provide a game semantics for the developed logic. The…
Soft linear logic ([Lafont02]) is a subsystem of linear logic characterizing the class PTIME. We introduce Soft lambda-calculus as a calculus typable in the intuitionistic and affine variant of this logic. We prove that the (untyped) terms…
We devise calculus rules for the Kurdyka-\L{}ojasiewicz exponent using the rank theorem and Lie group actions. They apply to a wide class of composite and invariant functions, and are particularly suitable for handling nonisolated local…
There has been renewed interest in recent years in McKinsey and Tarski's interpretation of modal logic in topological spaces and their proof that S4 is the logic of any separable dense-in-itself metric space. Here we extend this work to the…
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…
Satisfiability checking for monotone modal logic is known to be (only) NP-complete. We show that this remains true when the logic is extended with aconjunctive and alternation-free fixpoint operators as well as the universal modality; the…
Justification Logics provide a framework for reasoning about justifications and evidences. Most of the accounts of justification logics are crisp in the sense that agent's justifications for a statement is convincing or is not. In this…
The first system of many-valued logic was introduced by J. Lukasiewicz, his motivation was of philosophical nature as he was looking for an interpretation of the concepts of possibility and necessity. Since then, plenty of research has been…
We present a logic for Proximity-based Understanding of Conditionals (PUC-Logic) that unifies the Counterfactual and Deontic logics proposed by David Lewis. We also propose a natural deduction system (PUC-ND) associated to this new logic.…
We report on COOL-MC, a model checking tool for fixpoint logics that is parametric in the branching type of models (nondeterministic, game-based, probabilistic etc.) and in the next-step modalities used in formulae. The tool implements…
Mechanisms for the automation of uncertainty are required for expert systems. Sometimes these mechanisms need to obey the properties of probabilistic reasoning. A purely numeric mechanism, like those proposed so far, cannot provide a…
Possibilistic computation tree Logic (PoCTL) is one kind of branching temporal logic combined with uncertain information in possibility theory, which was introduced in order to cope with the systematic verification on systems with uncertain…
The paper presents probabilistic extensions of interval temporal logic (ITL) and duration calculus (DC) with infinite intervals and complete Hilbert-style proof systems for them. The completeness results are a strong completeness theorem…