John-Jules Ch. Meyer

Graded Modalities in Epistemic Logic

We propose an epistemic logic with so-called graded modalities, in which certain types of knowledge are expressible that are less absolute than in traditional epistemic logic. Beside ‘absolute knowledge’ (which does not allow for any exception), we are also able to express ‘accepting ϕ if there at most n exceptions to ϕ’. This logic may be employed in decision support systems where there are different sources to judge the same proposition. We argue that the logic also provides a link between epistemic logic and the more quantitative (even probabilistic) methods used in AI systems. In this paper we investigate some properties of the logic as well as some applications.

Formal Semantics of Temporal Epistemic Reflection

In this paper we show how a formal semantics can be given to reasoning processes in meta-level architectures that reason about (object level) knowledge states and changes of them. Especially the attention is focused on the upward and downward reflections in these architectures. Temporalized epistemic logic is used to specify meta-level reasoning processes and the outcomes of these.

Correctness of Programs with Function Procedures

The correctness of programs with programmer-declared functions is investigated. We use the framework of the typed lambda calculus with explicit declaration of (possibly recursive) functions. Its expressions occur in the statements of a simple language with assignment, composition and conditionals. A denotational and an operational semantics for this language are provided, and their equivalence is proved. Next, a proof system for partial correctness is presented, and its soundness is shown. Completeness is then established for the case that only call-by-value is allowed. Allowing call-by-name as well, completeness is shown only for the case that the type structure is restricted, and at the cost of extending the language of the proof system. The completeness problem for the general case remains open. In the technical considerations, an important role is played by a reduction system which essentially allows us to reduce expression evaluation to systematic execution of auxiliary assignments. Termination of this reduction system is shown using Taits computability technique. Complete proofs will appear in the full version of the paper.

Linear Time and Branching Time Semantics for Recursion with Merge

We consider two ways of assigning semantics to a class of statements built from a set of atomic actions (the ‘alphabet‘), by means of sequential composition, nondeterministic choice, recursion and merge (arbitrary interleaving). The first is linear time semantics (LT), stated in terms of trace theory; the semantic domain is the collection of all closed sets of finite and infinite words. The second is branching time semantics (BT), as introduced by de Bakker and Zucker; here the semantic domain is the metric completion of the collection of finite processes. For LT we prove the continuity of the operations (merge, sequential composition) in a direct, combinatorial way.

Towards an Epistemic Approach to Reasoning about Concurrent Programs

We show how epistemic logic may be used to reason about concurrent programs. Starting out from Halpern & Moses interpretation of knowledge in the context of distributed systems, where they use the interleaving model, we extend this to a setting where also truly concurrent computations can be modelled, viz. posets of action labels. Moreover, and more importantly, we prepare grounds for the verification of concurrent programs. We focus on a variant of the well-known 1978-version of Hoares Concurrent Sequential Processes (CSP) to see how the details work out for a concrete and simple language.

Infinite Streams and Finite Observations in the Semantics of Uniform Concurrency

Two ways of assigning meaning to a language with uniform concurrency are presented and compared. The language has uninterpreted elementary actions from which statements are composed using sequential composition, nondeterministic choice, parallel composition with communication, and recursion. The first semantics uses infinite streams in the sense which is a refinement of the linear time semantics of De Bakker et al. The second semantics uses the finite observations of Hoare et al., situated “in between” the divergence and readiness semantics of Olderog & Hoare. It is shown that the two models are isomorphic and that this isomorphism induces an equivalence result between the two semantics.