Related papers: Relational Dualities and Bisimulation
Theoretical equivalence and duality are two closely related notions: but their interconnection has so far not been well understood. In this paper I explicate the contribution of a recent schema for duality to discussions of theoretical…
Relational descriptions have been used in formalizing diverse computational notions, including, for example, operational semantics, typing, and acceptance by non-deterministic machines. We therefore propose a (restricted) logical theory…
We identify and highlight certain landmark results in Samson Abramsky's work which we believe are fundamental to current developments and future trends. In particular, we focus on the use of (i) topological duality methods to solve problems…
We display a family of Stone-type dualities linking categories of frames carrying pairs of modal operators to categories of spaces carrying a binary relation. Different notions of morphism used on the relational side lead to significant…
Provability logic GLP is well-known to be incomplete w.r.t. Kripke semantics. A natural topological semantics of GLP interprets modalities as derivative operators of a polytopological space. Such spaces satisfying all the axioms of GLP are…
We define a model for linear logic based on two well-known ingredients: games and simulations. This model is interesting in the following respect: while it is obvious that the objects interpreting formulas are games and that everything is…
A logic is defined that allows to express information about statistical probabilities and about degrees of belief in specific propositions. By interpreting the two types of probabilities in one common probability space, the semantics given…
The paper describes an extension of well-founded semantics for logic programs with two types of negation. In this extension information about preferences between rules can be expressed in the logical language and derived dynamically. This…
It is known that intuitionistic Kripke semantics can be generalized so that it can treat arbitrary propositional connectives characterized by truth functions. We extend this generalized Kripke semantics to first-order logic, and study how…
In this work we study the decidability of a class of global modal logics arising from Kripke frames evaluated over certain residuated lattices, known in the literature as modal many-valued logics. We exhibit a large family of these modal…
Many behavioural equivalences or preorders for probabilistic processes involve a lifting operation that turns a relation on states into a relation on distributions of states. We show that several existing proposals for lifting relations can…
We introduce a new form of logical relation which, in the spirit of metric relations, allows us to assign each pair of programs a quantity measuring their distance, rather than a boolean value standing for their being equivalent. The…
Separation logic is a concise method for specifying programs that manipulate dynamically allocated storage. Partially inspired by separation logic, Implicit Dynamic Frames has recently been proposed, aiming at first-order tool support. In…
Program transformations are widely used in synthesis, optimization, and maintenance of software. Correctness of program transformations depends on preservation of some important properties of the input program. By regarding programs as…
Kripke frames (and models) provide a suitable semantics for sub-classical logics, for example Intuitionistic Logic (of Brouwer and Heyting) axiomatizes the reflexive and transitive Kripke frames (with persistent satisfaction relations), and…
In the same sense as classical logic is a formal theory of truth, the recently initiated approach called computability logic is a formal theory of computability. It understands (interactive) computational problems as games played by a…
With the technology of the time, Kowalski's seminal 1974 paper {\em Predicate Logic as a Programming Language} was a breakthrough for the use of logic in computer science. It introduced two fundamental ideas: on the declarative side, the…
This paper explores proof-theoretic semantics, a formal approach to inferential semantics. It derives sentence meaning from formalized proofs, building upon Gentzen and Prawitz's work. The study addresses challenges in understanding how…
Several notions of bisimulation relations for probabilistic non-deterministic transition systems have been considered in the literature. We consider a novel testing-based behavioral equivalence called upper-expectation bisimilarity and…
The logic of definitions is a family of logics for encoding and reasoning about judgments, which are atomic predicates specified by inference rules. A definition associates an atomic predicate with a logical formula, which may itself depend…