Abstract State Machines

Abstract

Abstract:We introduce a logic for non distributed, deterministic Abstract State Machines with parallel function updates. Unlike other logics for ASMs which are based on dynamic logic, our logic is based on an atomic predicate for function updates and on a definedness predicate for the termination of the evaluation of transition rules. We do not assume that the transition rules of ASMs are in normal form, for example, that they concern distinct cases. Instead we allow structuring concepts of ASM rules including sequential composition and possibly recursive submachine calls. We show that several axioms that have been proposed for reasoning about ASMs are derivable in our system. We provide also an extension of the logic with explicit step information which allows to eliminate modal operators in certain cases. The main technical result is that the logic is complete for hierarchical (non-recursive) ASMs. We show that, for hierarchical ASMs, the logic is a definitional extension of first-order predicate logic.

Ibn Sīnā on Analysis: 1. Proof Search. Or: Abstract State Machines as a Tool for History of Logic

“…The four sentence types are as follows, together with their names and their truth conditions: (6) • Universally quantified affirmative, 'Every A is a B'. This counts as true if there are As, but there are no As that are not Bs, and false otherwise.…”

“…A syllogistic sentence of the form 'Every A is a B' is got by putting common nouns in place of 'A' and 'B', with the sole restriction that the two common nouns must have different meanings. By 'syllogistic sentence' we will mean a sentence of one of the four forms in (6).…”

“…But they can be proved directly from the truth conditions in (6). Ibn Sīnā himself probably knew Theorem 1 from experience, though it's hard to see how he could have proved it.…”

3-Level Service Composition and Cashew: A Model for Orchestration and Choreography in Semantic Web Services

“…So far in WSMO, the formal basis of orchestration and choreography in the form of abstract state machines (ASM s) [2] has been prescribed. Thereafter use of ASM choreographies to define the protocol that a client must use in order to consume a service has been defined [9] and exemplified [11].…”

Definition and Correct Refinement of Operation Specifications

“…The contract prescribes how for a given pre-state the post-state is constructed. Well-known examples for constructive languages are Abstract State Machines (ASMs) [14], B [15], and UML's Action Language [16].…”