Related papers: Weighted propositional configuration logics: A spe…
In traditional justification logic, evidence terms have the syntactic form of polynomials, but they are not equipped with the corresponding algebraic structure. We present a novel semantic approach to justification logic that models…
In the refinement calculus, monotonic predicate transformers are used to model specifications for (imperative) programs. Together with a natural notion of simulation, they form a category enjoying many algebraic properties. We build on this…
We show that context semantics can be fruitfully applied to the quantitative analysis of proof normalization in linear logic. In particular, context semantics lets us define the weight of a proof-net as a measure of its inherent complexity:…
Modern answer set programming solvers such as CLINGO support advanced language constructs that improve the expressivity and conciseness of logic programs. Conditional literals are one such construct. They form "subformulas" that behave as…
Choice constructs are an important part of the language of logic programming, yet the study of their semantics has been a challenging task. So far, only two-valued semantics have been studied, and the different proposals for such semantics…
This note is concerned with a formal analysis of the problem of non-monotonic reasoning in intelligent systems, especially when the uncertainty is taken into account in a quantitative way. A firm connection between logic and probability is…
The paper introduces a propositional linguistic logic that serves as the basis for automated uncertain reasoning with linguistic information. First, we build a linguistic logic system with truth value domain based on a linear symmetrical…
Over the last 20 years a large number of automata-based specification theories have been proposed for modeling of discrete,real-time and probabilistic systems. We have observed a lot of shared algebraic structure between these formalisms.…
We study counting propositional logic as an extension of propositional logic with counting quantifiers. We prove that the complexity of the underlying decision problem perfectly matches the appropriate level of Wagner's counting hierarchy,…
Lawvere showed that generalised metric spaces are categories enriched over $[0, \infty]$, the quantale of the positive extended reals. The statement of enrichment is a quantitative analogue of being a preorder. Towards seeking a logic for…
Finding a denotational semantics for higher order quantum computation is a long-standing problem in the semantics of quantum programming languages. Most past approaches to this problem fell short in one way or another, either limiting the…
We introduce propositional team-based logics expressively complete for (quasi) downward and (quasi) upward closed properties in a syntactically dual way, by using variants of the inclusion atom. In particular, the variants of the primitive…
We show that descriptive complexity's result extends in High Order Logic to capture the expressivity of Turing Machine which have a finite number of alternation and whose time or space is bounded by a finite tower of exponential. Hence we…
The assignment of weights to attacks in a classical Argumentation Framework allows to compute semantics by taking into account the different importance of each argument. We represent a Weighted Argumentation Framework by a non-binary…
Fagin's seminal result characterizing $\mathsf{NP}$ in terms of existential second-order logic started the fruitful field of descriptive complexity theory. In recent years, there has been much interest in the investigation of quantitative…
Probabilistic programming provides a convenient lingua franca for writing succinct and rigorous descriptions of probabilistic models and inference tasks. Several probabilistic programming languages, including Anglican, Church or Hakaru,…
Rewriting logic is naturally concurrent: several subterms of the state term can be rewritten simultaneously. But state terms are global, which makes compositionality difficult to achieve. Compositionality here means being able to decompose…
The reasoning with qualitative uncertainty measures involves comparative statements about events in terms of their likeliness without necessarily assigning an exact numerical value to these events. The paper is divided into two parts. In…
Logic has proved essential for formally modeling software based systems. Such formal descriptions, frequently called specifications, have served not only as requirements documentation and formalisation, but also for providing the…
Due to the increased complexity of software development projects more and more systems are described by models. The sheer size makes it impractical to describe these systems by a single model. Instead many models are developed that provide…