Related papers: Reasoning About Bounds in Weighted Transition Syst…
Large language models (LLMs) have demonstrated remarkable reasoning capabilities when prompted with strategies such as Chain-of-Thought (CoT). However, these approaches focus on token-level output without considering internal weight…
We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…
In previous works, a tableau calculus has been defined, which constitutes a decision procedure for hybrid logic with the converse and global modalities and a restricted use of the binder. This work shows how to extend such a calculus to…
There has been a long history of using fuzzy language equivalence to compare the behavior of fuzzy systems, but the comparison at this level is too coarse. Recently, a finer behavioral measure, bisimulation, has been introduced to fuzzy…
Propositional term modal logic is interpreted over Kripke structures with unboundedly many accessibility relations and hence the syntax admits variables indexing modalities and quantification over them. This logic is undecidable, and we…
Transformers are ubiquitous models in the natural language processing (NLP) community and have shown impressive empirical successes in the past few years. However, little is understood about how they reason and the limits of their…
We first study labeled transition systems with explicit successful termination. We establish the notions of strong, weak, and branching bisimulation in terms of boolean matrix theory, introducing thus a novel and powerful algebraic…
This paper introduces a new behavioral system model with distinct external and internal signals possibly evolving on different time scales. This allows to capture abstraction processes or signal aggregation in the context of control and…
Generalized topological spaces are not necessarily closed under finite intersections. Moreover, the whole universe does not need to be open. We use modified version of this framework to establish certain models for non-normal modal logics.…
We develop a new bisimulation (pseudo)metric for weighted finite automata (WFA) that generalizes Boreale's linear bisimulation relation. Our metrics are induced by seminorms on the state space of WFA. Our development is based on spectral…
We present a modal logic based approach to the so-called endophysical quantum universe. In particular, we treat the problem of preferred bases and that of state reduction by employing an eclectic collection of methods including Baltag's…
The limited version of bisimulation, called limited approximate bisimulation, has recently been introduced to fuzzy transition systems (NFTSs). This article extends limited approximate bisimulation to NFTSs, which are more general…
Weighted automata are nondeterministic automata with numerical weights on transitions. They can define quantitative languages~$L$ that assign to each word~$w$ a real number~$L(w)$. In the case of infinite words, the value of a run is…
The unbounded knapsack problem with bounded weights is a variant of the well-studied variant of the traditional binary knapsack problem; key changes being the relaxation of the binary constraint and allowing the unit weights of each item to…
We introduce the calculus of Classical Transitions (CT), which extends the research line on the relationship between linear logic and processes to labelled transitions. The key twist from previous work is registering parallelism in typing…
This paper studies the relationships between three notions of behavioural preorder that have been proposed in the literature: refinement over modal transition systems, and the covariant-contravariant simulation and the partial bisimulation…
We introduce the concept of weighted rules under the stable model semantics following the log-linear models of Markov Logic. This provides versatile methods to overcome the deterministic nature of the stable model semantics, such as…
When the experimental objective is expressed by a set of estimable functions, and any eigenvalue-based optimality criterion is selected, we prove the equivalence of the recently introduced weighted optimality and the 'standard' optimality…
We compare two recent extensions of the answer set (stable model) semantics of logic programs. One of them, due to Lifschitz, Tang and Turner, allows the bodies and heads of rules to contain nested expressions. The other, due to Niemela and…
In the style of Lindstr\"om's theorem for classical first-order logic, this article characterizes propositional bi-intuitionistic logic as the maximal (with respect to expressive power) abstract logic satisfying a certain form of…