Term-modal logic and quantifier-free dynamic assignment logic

Sammanfattning: In this dissertation, we present two new sorts of computer sciencelogics. Many powerful logics exist today for reasoning about multi-agentsystems, but in most of these it is hard to reason about an infiniteor indeterminate number of agents. Also the naming schemes used inthe logics often lack expressiveness to name agents in an intuitiveway. To obtain a more expressive language for multi-agent reasoning and abetter naming scheme for agents, we introduce in the first part of thedissertation a family of logics called term-modal logics. A mainfeature of our logics is the use of modal operators indexed by theterms of the logics. Thus, one can quantify over variables occurringin modal operators. In term-modal logics agents can be represented byterms, and knowledge of agents is expressed with formulas within thescope of modal operators. This gives us a flexible and uniform language for reasoning about theagents themselves and their knowledge. We give examples of theexpressiveness of the languages and provide sequent-style andtableau-based proof systems for the logics. Furthermore, we giveproofs of soundness and completeness with respect to the possibleworld semantics. In the second part of the dissertation, we treat another problem inreasoning about multi-agent systems, namely the problem of informationupdating. We develop a dynamic logic of assignments with a scopingoperator instead of quantifiers. Function, relation symbols and logicvariables are all rigidly interpreted in our semantics, while programvariables are non-rigid. The scoping operator is used to distinguishbetween the value of a program variable before and after the executionof a program. We provide a tableau proof system for the logic. First, the system isproved complete without the star operator, and then with the staroperator using an omega rule. The full logic is shown to beundecidable, while some interesting fragments are decidable.