Multi-adjoint logic programs generalise monotonic and residuated logic programs [2] in that simultaneous use of several implications in the rules and rather general connectives in the bodies are allowed. As our approach has continuous fixpoint semantics, in this work, a procedural semantics is given for the paradigm of multi-adjoint logic programming and a completeness result is proved. Some ap...

Monoidal t-norm based logic MTL is the logic of left continuous t-norms. We introduce two analytic calculi for first-order MTL. These are obtained by lifting two sequent calculi for different fragments of this logic to the hypersequent level with subsequent addition of Avron’s communication rule. Our calculi enable to prove the mid(hyper)sequent theorem. As corollaries follow Herbrand’s theorem...

It is common practice in both theoretical computer science and theoretical physics to describe the (static) logic of a system by means of a complete lattice. When formalizing the dynamics of such a system, the updates of that system organize themselves quite naturally in a quantale, or more generally, a quantaloid. In fact, we are lead to consider cocomplete quantaloid-enriched categories as fu...

Scott’s information systems provide a categorically equivalent, intensional description of Scott domains and continuous functions. Following a well established pattern in denotational semantics, we define a linear version of information systems, providing a model of intuitionistic linear logic (a newSeely category), with a “set-theoretic” interpretation of exponentials that recovers Scott conti...

In the last decade remarkable progress has been made on combining statistical machine learning techniques, reasoning under uncertainty, and relational representations. The branch of Artificial Intelligence working on the synthesis of these three areas is known as statistical relational learning or probabilistic logic learning. ProbLog, one of the probabilistic frameworks developed, is an extens...

The role played by continuous morphisms in propositional modal logic is investigated: it turns out that they are strictly related to filtrations and to suitable variants of the notion of a free algebra. We also employ continuous morphisms in the incremental construction of (standard) finitely generated free S4-algebras. This Technical Report reproduces the content of my talk given at the worksh...

The paper analyzes dynamic epistemic logic from a topological perspective. The main contribution consists of a framework in which dynamic epistemic logic satisfies the requirements for being a topological dynamical system thus interfacing discrete dynamic logics with continuous mappings of dynamical systems. The setting is based on a notion of logical convergence, demonstratively equivalent wit...

This paper proposes a novel abstraction technique for continuous-time Markov chains (CTMCs). Our technique fits within the realm of three-valued abstraction methods that have been used successfully for traditional model checking. The key idea is to apply abstraction on uniform CTMCs that are readily obtained from general CTMCs, and to abstract transition probabilities by intervals. It is shown ...

this paper submitting the computation of optimize point of ordering in inventory control systems and particularly for continuous review of ordering system (r,q) by fuzzy logic method which similarly can be used for other ordering systems. since in the ordering models we cannot forecast the parameters like cost exactly, we have ambiguity. in this case using precise parameters may cause wrong dec...