Related papers: {\L}ukasiewicz mu-Calculus
In [11] we defined Inf-Datalog and characterized the fragments of Monadic inf-Datalog that have the same expressive power as Modal Logic (resp. $CTL$, alternation-free Modal $\mu$-calculus and Modal $\mu$-calculus). We study here the time…
The multi-valued logic of {\L}ukasiewicz is a substructural logic that has been widely studied and has many interesting properties. It is classical, in the sense that it admits the axiom schema of double negation, [DNE]. However, our…
The paper is a contribution both to the theoretical foundations and to the actual construction of efficient automatizable proof procedures for non-classical logics. We focus here on the case of finite-valued logics, and exhibit: (i) a…
A key result in the theory of the modal mu-calculus is the disjunctive normal form theorem by Janin & Walukiewicz, stating that every mu-calculus formula is semantically equivalent to a so-called disjunctive formula. These disjunctive…
Differentiable logics are a family of quantitative logics originated in the machine learning literature. Because of their origin, differentiable logics often come equipped with analytic properties that guarantee that they are…
In probabilistic transition systems, behavioural metrics provide a more fine-grained and stable measure of system equivalence than crisp notions of bisimilarity. They correlate strongly to quantitative probabilistic logics, and in fact the…
A probabilistic propositional logic, endowed with an epistemic component for asserting (non-)compatibility of diagonizable and bounded observables, is presented and illustrated for reasoning about the random results of projective…
The analysis and control of stochastic dynamical systems rely on probabilistic models such as (continuous-space) Markov decision processes, but large or continuous state spaces make exact analysis intractable and call for principled…
The use of exponentials in linear logic greatly enhances its expressive power. In this paper we focus on nonassociative noncommutative multiplicative linear logic, and systematically explore modal axioms K, T, and 4 as well as the…
We combine the concepts of modal logics and many-valued logics in a general and comprehensive way. Namely, given any finite linearly ordered set of truth values and any set of propositional connectives defined by truth tables, we define the…
Cirquent calculus is a proof system with inherent ability to account for sharing subcomponents in logical expressions. Within its framework, this article constructs an axiomatization CL18 of the basic propositional fragment of computability…
Following A. Kuznetsov's outline, we restore Kuznetsov's syntactic proof of the assertoric equipollence of the intuitionistic propositional calculus and the proof-intuitionistic calculus KM (Kuznetsov's Theorem). Then, we show that this…
In this paper, we propose a new logic for expressing and reasoning about probabilistic hyperproperties. Hyperproperties characterize the relation between different independent executions of a system. Probabilistic hyperproperties express…
We investigate logics and equivalence relations that capture the qualitative behavior of Markov Decision Processes (MDPs). We present Qualitative Randomized CTL (QRCTL): formulas of this logic can express the fact that certain temporal…
Analytic proof calculi are introduced for box and diamond fragments of basic modal fuzzy logics that combine the Kripke semantics of modal logic K with the many-valued semantics of G\"odel logic. The calculi are used to establish…
In this paper, we investigate the many-valued version of coalgebraic modal logic through predicate lifting approach. Coalgebras, understood as generic transition systems, can serve as semantic structures for various kinds of modal logics. A…
Baaz's operator $\Delta$ was introduced (by Baaz) in order to extend G\"odel logics, after that this operator was used to expand fuzzy logics by H\'ajek in his celebrated book. These logics were called $\Delta$-fuzzy logics. On the other…
Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal…
We introduce PHFL, a probabilistic extension of higher-order fixpoint logic, which can also be regarded as a higher-order extension of probabilistic temporal logics such as PCTL and the $\mu^p$-calculus. We show that PHFL is strictly more…
We consider bisimulation-invariant monadic second-order logic over various classes of finite transition systems. We present several combinatorial characterisations of when the expressive power of this fragment coincides with that of the…