A logic for propositions with indefinite truth values

In the first part of this paper a logic is defined for propositions whose probability of being true may not be known. A speaker's beliefs about which propositions are true are still interesting in this case. The meaning of propositions is determined by the consequences of asserting them: in this logic there are debates which incur certain costs for the protagonists.The second part of the paper describes the mathematics of the resulting logic which displays several novel features.     

Beliefs and values as possible correlates of ethical awareness in business

The relationship between retailing students' beliefs and values about life and their reactions to and perceptions of ethical dilemmas in retailing settings was investigated. One hundred and two male and female college students majoring in retailing were asked to complete the Beliefs and Values Questionnaire (BVQ) and to indicate their agreement with a variety of actions taken in retailing situations. Participants were also asked to indicate the extent to which the scenarios presented were representative of ethical problems or issues. With a few exceptions, results of this exploratory study did not support the contention that beliefs and values, as a measure of ethical orientation, are related to one's perception of retailing scenarios as either ethical or unethical. Discussion focuses on the need for more rigorous, systematic research to identify the correlates of ethical or unethical behavior and also the need for more direct investigation of the link between ethical decision making and students' ethical orientation. It is argued that such research is necessary as a prerequisite to ethics education.The author expresses gratitude to the College for Human Development at Syracuse University for initial funding for this project.     

Deontic logic and possible worlds semantics: A historical sketch

This paper describes and compares the first step in modern semantic theory for deontic logic which appeared in works of Stig Kanger, Jaakko Hintikka, Richard Montague and Saul Kripke in late 50s and early 60s. Moreover, some further developments as well as systematizations are also noted.     

A free IPC is a natural logic: Strong completeness for some intuitionistic free logics

IPC, the intuitionistic predicate calculus, has the property

1. Vc(Γ?A ^c /x) ? Γ??xA.Furthermore, for certain important Γ, IPC has the converse property
2. Γ??xA ? Vc(Γ?A ^c /x).
3. may be given up in various ways, corresponding to different philosophic intuitions and yielding different systems of intuitionistic free logic. The present paper proves the strong completeness of several of these with respect to Kripke style semantics. It also shows that giving up (i) need not force us to abandon the analogue of (ii).

     

Quantum logic as a dynamic logic

We address the old question whether a logical understanding of Quantum Mechanics requires abandoning some of the principles of classical logic. Against Putnam and others (Among whom we may count or not E. W. Beth, depending on how we interpret some of his statements), our answer is a clear “no”. Philosophically, our argument is based on combining a formal semantic approach, in the spirit of E. W. Beth’s proposal of applying Tarski’s semantical methods to the analysis of physical theories, with an empirical–experimental approach to Logic, as advocated by both Beth and Putnam, but understood by us in the view of the operational- realistic tradition of Jauch and Piron, i.e. as an investigation of “the logic of yes–no experiments” (or “questions”). Technically, we use the recently-developed setting of Quantum Dynamic Logic (Baltag and Smets 2005, 2008) to make explicit the operational meaning of quantum-mechanical concepts in our formal semantics. Based on our recent results (Baltag and Smets 2005), we show that the correct interpretation of quantum-logical connectives is dynamical, rather than purely propositional. We conclude that there is no contradiction between classical logic and (our dynamic reinterpretation of) quantum logic. Moreover, we argue that the Dynamic-Logical perspective leads to a better and deeper understanding of the “non-classicality” of quantum behavior than any perspective based on static Propositional Logic.     

A second-order relevance logic with modality

In this paper a system, RPF, of second-order relevance logic with S5 necessity is presented which contains a defined, notion of identity for propositions. A complete semantics is provided. It is shown that RPF allows for more than one necessary proposition. RPF contains primitive syntactic counterparts of the following semantic notions: (1) the reflexive, symmetrical, transitive binary alternativeness relation for S5 necessity, (2) the ternary Routley-Meyer alternativeness relation for implication, and (3) the Routley-Meyer notion of a prime intensional theory, as well as defined syntactic counterparts, of the semantic notions of a possible world and the Routley-Meyer ^* operator.     

The logic of algebraic rules as a generalization of equational logic

In this paper we start an investigation of a logic called the logic of algebraic rules. The relation of derivability of this logic is defined on universal closures of special disjunctions of equations extending the relation of derivability of the usual equational logic. The paper contains some simple theorems and examples given in justification for the introduction of our logic. A number of open questions is posed.     

A propositional logic with explicit fixed points

This paper studies a propositional logic which is obtained by interpreting implication as formal provability. It is also the logic of finite irreflexive Kripke Models.A Kripke Model completeness theorem is given and several completeness theorems for interpretations into Provability Logic and Peano Arithmetic.     

The logic of historical necessity as founded on two-dimensional modal tense logic

We consider a version of so called T × W logic for historical necessity in the sense of R.H. Thomason (1984), which is somewhat special in three respects: (i) it is explicitly based on two-dimensional modal logic in the sense of Segerberg (1973); (ii) for reasons of applicability to interesting fields of philosophical logic, it conceives of time as being discrete and finite in the sense of having a beginning and an end; and (iii) it utilizes the technique of systematic frame constants in order to handle the problem of irreflexivity in tense logics, well known since Gabbay (1981). Axiomatizations are given for two infinite hierarchies of two-dimensional modal tense logics, one without and one with the characteristic operators for historical necessity and possibility. Strong and weak completeness results are obtained for both hierarchies as well as a result to the effect that two approaches to their semantics are equivalent, much in the spirit of Di Maio and Zanardo (1996) and von Kutschera (1997).     

Intermediate logics with the same disjunctionless fragment as intuitionistic logic

Given an intermediate prepositional logic L, denote by L ^–d its disjuctionless fragment. We introduce an infinite sequence {J _n}_n1 of propositional formulas, and prove:(1)For any L: L ^–d =I ^–d (I=intuitionistic logic) if and only if J _n L for every n 1.Since it turns out that L{J _{n} n}1 = Ø for any L having the disjunction property, we obtain as a corollary that L ^–d = I ^–d for every L with d.p. (cf. open problem 7.19 of [5]). Algebraic semantic is used in the proof of the if part of (1). In the last section of the paper we provide a characterization in Kripke's semantic for the logics J _n =I+ +J _n (n 1).     

Predictability influences whether outcomes are processed in terms of original or relative values

Previous studies have provided insights into the representations of original and relative values and the influence of predictability on decision making. However, whether the predictability of outcomes can influence the processing manner of outcomes (i.e. whether the outcomes are processed in terms of original or relative values) is still unknown. To investigate this issue, we had participants perform a monetary decision task which resulted in two outcomes with the same relative values but different original values in either a predictable or unpredictable condition, while recording event-related potentials (ERP). ERP results showed that the outcome processing in the unpredictable condition elicited more positive deflections in the time window of 300–500 ms (P300) than did those in the predictable condition. More importantly, the outcome with high original value elicited a greater P300 component than did that with low original value in the unpredictable condition even though these two outcomes had the same relative values, while in the predictable condition no significant difference was observed between ERPs elicited by the two outcomes even though their original values were different. These results suggest that the outcomes might be processed in terms of relative values in the predictable condition but original values in the unpredictable condition.