Ian horrocks, ullrich hustadt, ulrike sattler, renate schmidt. Remember, p is a wff of pa, and h is a countable model of pa. Basic concepts in modal logic1 stanford university. At the talk, dana introduced a new, probabilistic semantics for modal logica semantics about which very little was known at the time. Philosophical issues from kripkes semantical considerations on modal logic 3 and the appeal to intuition intuitively do we have a recommendation to think of matters this way or not. Philosophical issues from kripkes semantical considerations on modal logic.
From the semantical point of view, we are confronted with a number of decisions concerning the quantifiers, and these in turn prompt new questions about the. The present paper attempts to extend the results of l, in the domain of the propositional calculus, to a class of modal systems called normal. Proceedings of a colloquium on modal and manyvalued logics, helsinki, 2326 august, 1962, acta. Alternative semantic systems for normal modal logics george weaver bryn mawr college this paper is a continuation of the investigations reported in weaver and corcoran 1971, where several semantic systems for s4 extensions of sentential logic were. Interestingly, the classical version of our logic is not a normal modal logic, even in the case of relational semantics. Rather, it was directed toward the development of a rigorous account of logical implication.
Modal logic is characterized by the modal operators box p asserting that is necessarily the case, and diamond p asserting that is possibly the case. Kripke, semantical considerations for modal logics gabbay, dov, journal of symbolic logic, 1969. We show how semantical considerations have allowed us to formulate nontrivial principles about formalized interpretability. On the other hand, the passage from local to global semantics is achieved if one looks at truth in all states an abstraction through implicit universal. Saul kripke and the course of modal logic 5 but over the years, modal logic has undergone some major changes, a. The semantics for modal logic that is announced and developed together with the. Saul kripke, semantical considerations of the modal logic.
There has been much philosophical discussion of whether endorsement of the kripke semantics brings ontological commitment to possible worlds. Exercises on this level show the connections between modal laws and quantifier logic regarding generalization into, or out of, modal contexts and the. Neighborhood semantics for modal logic an introduction. The novice may wonder why quantified modal logic qml is considered difficult. First, i will discuss the technical work that accessibility does in unifying and providing an extensional formal semantics for the plethora of modal logics that have come into existence since aristotle. The tableaux that leads to a decision procedure for the propositional calculi is considered. They have incorporated all the new developments that have taken place since 1968 in both modal propositional logic and modal predicate logic.
We define a model rp by requiring that, for any atomic formula p and h e k, rpp, h tf iff p is true false in the model h. We look at a few, and try to state their essence as a contribution to universal logic, i. Both a firstorder modal logic for possibilism containing actualism as a proper part as well as a separate modal logic for actualism alone are constructed for a variety of modal systems. Pdf to text batch convert multiple files software please purchase personal license. Schema theory and the analysis of text worlds in poetry.
This paper presents a multimodal language which is bisimulation invariant and under a natural completeness. In 1933 g odel introduced a calculus of provability also known as modal logic s4 and left open the question of its exact intended semantics. This chapter discusses semantical analysis of modal logic ii and nonnormal modal propositional calculi. Model theory of modal logic 3 over the given frame in e. Semantical considerations on modal logic, acta philosophica fennica 16. A completeness theorem in modal logic, journal of symbolic logic 241. A propositional modal logic of time intervals journal of. Unfortunately, this choice does not correspond to a intuitively satisfying semantics. In proceedings of the 6th annual symposium on the principles of programmmg languages. Modal logic deontic logic general frame semantic consequence modal algebra. Citeseerx document details isaac councill, lee giles, pradeep teregowda. A quantified modal logic is a set of axioms and rules of inference that systematizes the logical truths expressible in a firstorder modal language with identity. Home browse by title periodicals artificial intelligence vol.
In semantical considerations on modal logic, kripke articulates his project in the discourse of possible worlds. Proceedings of the 1963 international symposium at berkeley. Moore 1985, semantical constructions on nonmonotonic logic, ai j, 25, 7594. Computational modal logic introduction ps pdf authors. A semantic perspective 3 chapters in this handbook. Semantical considerations on modal logic 71 pa, g is the standard model in the natural numbers, and r is the cartesian product k2. Not everything is possible logic journal of the igpl. There are logicians, myself among them, to whom the ideas of modal logic e. View or download all content the institution has subscribed to. Strict implication april 6, 1998 modern modal logic did not begin as an attempt to clarify the notions of necessity and possibility. Unfortunately, this choice does not correspond to an intuitively satisfying semantics. Normal modal propositional calculi kaplan, david, journal of symbolic logic, 1966. Zakharyaschev, modal logic, oxford logic guides 35, clarendon press, 1997. This algebraic perspective dominated the semantical approach to modal logic until the publication of the groundbreaking works of kripke 30, 31.
There are interesting observations to make concerning the two systems. Modal logic is an extension of classic propositional and predicate logic that allows the use of modal operators. Semantical considerations on modal logic in reference and modality. Kripke, saul, naming and necessity, harvard university press, 1972. Semantical analysis of modal logic i normal modal propositional. Modal logic captures meaning beyond clearly statable facts. Moore 1983, semantical considerations on nonmonotonic logic, proc. In semantical considerations on modal logic, kripke articulates his project in. A new introduction to modal logic is an entirely new work, completely rewritten by the authors. Kripke, s 1963, semantical considerations in modal logic, acta philosophica fennica 16, 8394. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. Coalgebras for a functor on the category of sets subsume many formulations of the notion of transition system, including labelled transition systems, kripke models, kripke frames and many types of automata. Citeseerx semantical principles in the modal logic of. And, recommended or not, is the thought in question that this possibleworlds interpretation is distinguished from others by being the in.
Schema theory and the analysis of text worlds in poetry show all authors. What are the practical applications of modal logic. Pdf semantical considerations for a logic of actions. Semantical approach to cut elimination and subformula property in modal logic 15 cz97 a. Instead, we obtain a modal logic with both normal and nonnormal modalities, together with additional axiom that speci. An introduction to modal logic and a companion to modal logic. Alternatively, you can download the pdf file directly to your computer, from. It was first conceived for modal logics, and later adapted to intuitionistic logic and other nonclassical systems. Complexity of modal logic introduction ps pdf author. The main goal of the corse is to understand the basic techniques, results and applications of neighborhood semantics for modal logic and to understand the exact relationship with the standard relational semantics.
Module 3 basic syntax and semantics for modal sentential. Close actions are applied by default to all button actions, in addition an onapprove or ondeny callback will fire if the elements match either selector. Find, read and cite all the research you need on researchgate. A new semantics for positive modal logic celani, s. Semantical considerations on modal counterfactual logic with corollaries on decidability, completeness, and consistency questions. The atomic formulas of l have either the form px 1 x n, where p is nplace, or the form x y. Semantical considerations on modal logic divers principia. Semantical analysis of intuitionistic logic i sciencedirect. The choice of logical connectives depends on the development of propositional logic one wants to follow. We also consider the logic and semantics in classical setting. The proof of sufficiency, which is omitted by many, proceeds by constructing a normal characteristic matrix by lindenbaums method. Lewiss are not intuitively clear until explained in non. Philosophical issues from kripkes semantical considerations on. One of his major problems was the following reductionchallenge.
However, that discussion is less than satisfactory because it has been conducted without the necessary investigation of the. This logic is then compared with the system in kripkes semantical considerations on modal logic. Kripke, semantical considerations for modal logics. It often reflects possibility, desirability, clarity, plausibility or some other sought goal and simultaneously the restrictions on pursuing that goal, the kind of knowledge that someone has about what they are saying, that cannot be embedded meaningfully in the statement of the fact itself, but can only be alluded to. Semantical considerations on floydhoare logic in proceedings of the 17th annual symposium on foundatlons of computer science oct. A view of its evolution 5 was a variable neither always true nor always false. In particular we falsify the conjecture about the nature of the interpretability logic of all reasonable. Dynamic logic extends this by associating to every action the modal operators and, thereby making it a multimodal logic. Semantical considerations on modal logics, acta philoso. In this paper we discus work in progress on interpretability logics.
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