This is an advanced 2001 textbook on modal logic a field which caught the attention of computer scientists in the late 1970s. Researchers in areas ranging from economics to computational linguistics have since realised its worth.
Most controversial perhaps will be our decision to include modal and intuitionistic logic in an introductory text the inevitably cost being a rather more summary treatment of some aspects of classical predicate logic.
Modal logic computer science. None of the Axioms D T B 4 and 5 is Valid in the class of all standards models Proof. Logic in computer science is the speciﬁcation and veriﬁcation of software and hard-ware systems where modal logic appears eg in the guise of temporal logic and the propositional µ-calculus 54. Modal logic operators contain propositional logic operators such as conjunction and negation and operators that can have the following meanings.
We believe however that a glance at the wide variety of ways in which logic is used in computer science fully justifies this approach. This course offers a systematic exposition of fundamentals of modal logic together with an adjacent area of constructive reasoning. This modern advanced textbook reviews modal logic a field which caught the attention of computer scientists in the late 1970s.
The problem of logical omniscience 7. Leigh Lambert Edith Hemaspaandra Chair Chris Homan Reader Michael Van Wie Observer June 25 2004. Typically biological systems are reactive because they react to certain events.
Hintikkas Logic of Knowledge 6. Prior acquaintance with first-order logic and its semantics is assumed and familiarity with the basic mathematical notions of set theory is required. Modal logic is a widely applicable method of reasoning for many areas of computer science.
A displaystyle a and. Finally contemporary modal logic is profoundly influenced by its applications particularly in theoretical computer science. Completeness and Decidability 4.
This logic is complete for the class for all Kripke structures of the form m S m R m a m h m where a m Ra. Necessitation is dropped so although K 1 A A we can still have K 1 A A. Modal logic originated in the domain of Philosophy but during the past decades became a vibrant area with fundamental applications in computer science AI mathematics epistemology etc.
Progress 1 Introduction 2 Modal Logics 3 Model Theory 4 Axiomatic Theory 5 Main Modal Systems 6 Axioms and Class of Models 7 A Knowledge and Belief Logic 22 40 SG Models and Formalisms 42. The main reason for modal logic to be an eective tool in computer science is. Lecture 1 8 Basic modal logic.
A reactive system is a system that responds reacts to external events. φ pProp φ φ1 φ2 φ MGS Modal Logic. However the term is used primarily for describing human-made systems.
P is true in all possible worlds. Modal logic is a widely applicable method of reasoning for many areas of computer science. 3 Fuzzy Modal Logic Kripke semantics for modal logic consist of graphs labelled with propositional sym- bols on each edge.
Common Knowledge 9. Is definable Well-formed formula φ. Hence they can be used to model many situations such as network science graph theory epistemic logic and also for reasoning about time beliefs computational systems etc.
It is enough for each axiom to. These areas include artiﬁcial intelligence database the-. A displaystyle langle arangle thereby making it a multimodal logic.
Indeed some of the most interesting advances in the subject for example the development of propositional dynamic logic and the investigation of modal logic from a complexity-theoretic standpoint were largely due to. It deals with the logical behavior of such modal locutions as must and might was and will ought and may. Propositional Dynamic Logic 5.
These areas include artificial intelligence database theory distributed systems program verification and cryptography theory. Modal logic is the study of the laws of inferencefor judgments such as it is necessary that it is possible thatK knows that K affirms that etc. Point of modal logic has been veri ed by recent techniques in modal logic in which the proposition necessarily p has been analyzed as.
Axioms and Class of Models Theorem. A set of propositional variables Propp 1 p2 Boolean connectives and and are definable Unary modality. The development is mathematical.
Knowledge and time 8. Modal Logic in Computer Science. Lecture 1 9 Just for completeness.
Modal logic is a broad and rapidly expanding area of logic with applications to such diverse areas as computer science linguistics and philosophy. Modal logic is useful for verification of reactive systems. Basic Modal Logic.
Consider the logic K 1 obtained by collecting all theorems of modal logic K together with the schema A A and the rule of modus ponens. Its roots lie in philosophyand linguistics but it has a suprisingly rich variety of applicationsin computer science. A p displaystyle ap is that after performing action.
The authors focus on the use of modal languages as tools to analyze the properties of relational structures including their algorithmic and algebraic aspects and applications to issues in logic and computer science such as completeness computability and complexity are considered.