Based on a notion of "companions to stit formulas" applied in other papers dealing with astit logics, we introduce "choice formulas" and "nested choice formulas" to prove the completeness theorems for dstit logics in a language with the dstit operator as the only non-truth-functional operator. The main logic discussed in this paper is the basic logic of dstit with multiple agents, other logics discussed include the basic logic of dstit with a single agent and some logics of dstit with multiple (...) agents each of which corresponds to a semantic condition concerning the number of possible choices for agents. (shrink)

We propose a theory of events and causes against the background of branching time. Notions discussed include possibility based on reality, transitions, events, determinacy, contingency, causes and effects. The main idea in defining causal relations is to introduce a certain preconditioning circumstance under which one event follows another. We also briefly compare this theory with some other theories.

We present a simple theory of actions against the background of branching time, based on which we propose two versions of an extended stit theory, one equipped with particular actions and the other with sets of such actions. After reporting some basic results of a formal development of such a theory, we briefly explore its connection to a version of branching ETL.

This paper presents a short survey of recent developments in stit theories, with an emphasis on combinations of stit and deontic logic, and those of stit and epistemic logic.

We present a theory of actions based on a theory of events in branching time, in which "particular" or "token" actions are taken to be sets of transitions from their initial states to the outcomes. We also present a simple theory of composition of events by which composite events can be formed out of other events. Various kinds of actions, including instantaneous group actions and sequential group actions, are introduced by way of composition, and an extended stit theory of agency (...) is proposed, in which the stit operators are combined or equipped with reified group actions. (shrink)

We present in this paper an axiomatization of Belnap and Perloff's stit theory (a logic of "seeing to it that") with a single agent. The idea of the proof is to apply the notion of companion sets--the same notion as used in another paper by the author that showed the decidability of stit theory with a single agent and Refref equivalence.

The purpose of this paper is to prove the decidability ofstit theory (a logic of seeing to it that) with a single agent andRefref Equivalence. This result is obtained through an axiomatization of the theory and a proof that it has thefinite model property. A notion ofcompanions to stit formulas is introduced and extensively used in the proof.

The main purpose of this paper is to prove that in every stit semantic structure that contains a busy choice sequence, neither does doing imply refraining from refraining from doing, nor does refraining from refraining from doing imply doing.

The purpose of this paper is to present some results instit theory, a theory of agency proposed by N. Belnap and M. Perloff. We will establish a correspondence between the numbers ofstit modalities and the complexity degrees ofbusy choice sequences in semantic structures, and consequently, a correspondence between the number of modes of actions/inactions instit theory and the complexity degrees ofbusy choice sequences in semantic structures.

This paper proves the finite model property and the finite axiomatizability of a class of normal modal logics extending K4.3. The frames for these logics are those for K4.3, in each of which every point has a bounded number of irreflexive successors if it is after an infinite ascending chain of (not necessarily distinct) points.

This paper presents a generalization of Fine’s completeness theorem for transitive logics of finite width, and proves the Kripke completeness of transitive logics of finite “suc-eq-width”. The frame condition for each finite suc-eq-width axiom requires, in rooted transitive frames, a finite upper bound of cardinality for antichains of points with different proper successors. The paper also presents a generalization of Rybakov’s completeness theorem for transitive logics of prefinite width, and proves the Kripke completeness of transitive logics of prefinite “suc-eq-width”. The (...) frame condition for each prefinite suc-eq-width axiom requires, in rooted transitive frames, a finite upper bound of cardinality for antichains of points that have a finite lower bound of depth and have different proper successors. We will construct continuums of transitive logics of finite suc-eq-width but not of finite width, and continuums of those of prefinite suc-eq-width but not of prefinite width. This shows that our new completeness results cover uncountably many more logics than Fine’s theorem and Rybakov’s theorem respectively. (shrink)

We prove some embedding theorems for classical conditional logic, covering 'finitely cumulative' logics, 'preferential' logics and what we call 'semi-monotonic' logics. Technical tools called 'partial frames' and 'frame morphisms' in the context of neighborhood semantics are used in the proof.

Any text can not leave the text the user exists, with the phenomenon of indirect discourse anaphora is no exception. Therefore, the phenomenon of indirect anaphora can not be studied only from the text itself, but also from the recipient of discourse processing and mental representation of discourse strategies such as perspective depth studies to explore the source of discourse coherence factors. Indirect anaphor is a special kind of anaphor that receives more and more attention these years. Based on previous (...) research findings, this paper mainly deals with the syntactic and semantic classifications of indirect anaphor and comes up with several theoretic frameworks in which it could be explained. The author believes that a text is not a text without its users. It is no exception for texts containing indirect anaphora. Therefore, a proper method of investigation into indirect anaphora should contain not only studies of the text, but also studies on how the text is processed and mentally represented by text users. (shrink)

In this paper we prove the uncompactness of every stit logic that contains a generalized refref conditional and is a sublogic of the stit logic with refref equivalence, a syntactical condition of uncompactness that covers infinitely many stit logics. This result is established through the uncompactness of every stit logic whose semantic structures contain no chain of busy choice sequences with cardinality , where is any natural number . The basic idea in the proof is to apply the notion of (...) companions to stit sentences in finding busy choice sequences in structures, and to make use of a relation between chains of busy choice sequences and generalized refref conditionals in connecting the two conditions of uncompactness mentioned above. (shrink)

In a legal expert system based on CBR (Case-Based Reasoning), legal statute rules are interpreted on the basis of precedents. This interpretation, because of its vagueness and uncertainty of the interpretation cannot be handled with the means used for crisp cases. In our legal expert system, on the basis of the facts of precedents, the statute rule is interpreted as a form of case rule, the application of which involves the concepts of membership and vagueness. The case rule is stored (...) in a data base by means of fuzzy frames. The inference based on a case rule is made by fuzzy YES and fuzzy NO, and the degree of similarity of cases. The system proposed here will be used for legal education; its main area of application is contract, especially in relation to the United Nations Convention on Contracts for the International Sale of Goods (CISG). (shrink)

Based on the branching time theory proposed by Prior and Thomason, this thesis is devoted to characterizing the causal aspect of agency by considering a sentence "$\alpha$ sees to it that A" as asserting a causal relation between a choice made by the agent $\alpha$ and a fact described in the sentence A. The phrase "see to it that" is abbreviated as stit. This thesis provides conceptual analyses of stit and develops some modal logics of stit in accordance with these (...) analyses. Theories of stit discussed in this thesis include B. Chellas' theory, Von Kutschera and Horty's theory, and Belnap and Perloff's theory. ;Chapters I-II focus on a conceptual examination of stit theories. We start with branching time theory, and develop a notion of possibility based on reality. After a discussion of Chellas' theory of stit and the controversial issue about stit closure under consequence, we introduce a notion of factual consequences of actions to serve as a basic interpretation of stit sentences. In order to back up this notion, we present a theory of events, a theory of causation and a theory of alternatives for agents in branching time. Using these theories, we interpret the relation between actions and their factual consequences as a causal relation, i.e., factual consequences of actions are sentences describing facts that are caused by those actions. Finally we reach the same semantics for stit as those proposed by Von Kutschera and Horty, and Belnap and Perloff. In Chapters III-VI, we focus on the technical aspect of the stit theory proposed by Belnap and Perloff. We present an axiomatization of the basic logic ${\bf L}\sb0$ of stit with a single agent and prove its completeness, and present an axiomatization of the logic ${\bf L}\sb1$ of stit with a single agent and refref equivalence and prove its completeness and decidability. Finally we present a study of stit modalities which serves as a study of modes of actions/inactions as well as a preparation for further studies of logics between ${\bf L}\sb0$ and ${\bf L}\sb1.$. (shrink)