Proof-Theoretic Analysis of the Logics of Agency: The Deliberative STIT

Studia Logica - A sequent calculus methodology for systems of agency based on branching-time frames with agents and choices is proposed, starting with a complete and cut-free system for multi-agent...     

Does the deduction theorem fail for modal logic?

Various sources in the literature claim that the deduction theorem does not hold for normal modal or epistemic logic, whereas others present versions of the deduction theorem for several normal modal systems. It is shown here that the apparent problem arises from an objectionable notion of derivability from assumptions in an axiomatic system. When a traditional Hilbert-type system of axiomatic logic is generalized into a system for derivations from assumptions, the necessitation rule has to be modified in a way that restricts its use to cases in which the premiss does not depend on assumptions. This restriction is entirely analogous to the restriction of the rule of universal generalization of first-order logic. A necessitation rule with this restriction permits a proof of the deduction theorem in its usual formulation. Other suggestions presented in the literature to deal with the problem are reviewed, and the present solution is argued to be preferable to the other alternatives. A contraction- and cut-free sequent calculus equivalent to the Hilbert system for basic modal logic shows the standard failure argument untenable by proving the underivability of ${\square\,A}$ from A.     

Who was that masked man? Conjoint representations of intrinsic motions with actor appearance

Motion plays an important role in recognising animate creatures. This research supports a distinction between intrinsic and extrinsic motions in their relationship to identifying information about the characters performing the motions. Participants viewed events involving costumed human characters. Intrinsic motions involved relative movements of a character’s body parts, whereas extrinsic motions involved movements with respect to external landmarks. Participants were later tested for recognition of the motions and who had performed them. The critical test items involved familiar characters performing motions that had previously been performed by other characters. Participants falsely recognised extrinsic conjunction items, in which characters followed the paths of other characters, more often than intrinsic conjunction items, in which characters moved in the manner of other characters. In contrast, participants falsely recognised new extrinsic motions less often than new intrinsic motions, suggesting that they remembered extrinsic motions but had difficulty remembering who had performed them. Modelling of receiver operating characteristics indicated that participants discriminated old items from intrinsic conjunction items via familiarity, consistent with conjoint representations of intrinsic motion and identity information. In contrast, participants used recollection to distinguish old items from extrinsic conjunction items, consistent with separate but associated representations of extrinsic motion and identity information.     

Is systemic thinking really extraneous to common sense?

Systemic therapists assume, but have not yet proved that ordinary people: (i) normally do not use triadic thinking and (ii) are able, thanks to therapists' interviewing techniques, to construct triadic explanations. To test these assumptions this study analyses the explanations provided by 400 undergraduates of an unexpected piece of behaviour framed in four stimulus situations where the breadth of the observation field was manipulated. The results show that triadic explanations are unusual and increase with the widening of the field of observation from the monad to the triad. It is the ‘enigmatic’ triadic situation – adding a puzzling discrepancy between the actors' forms of behaviour – that elicits more triadic explanations. This suggests that therapists should explore with clients the contradictions disclosed by the widening of the field of observation and support reframings actively co‐constructed with them instead of ‘pre‐packaged’ ones.     

Beyond Pro-Social Behaviour: An Exploration of Altruism in Two Cultures

Altruism is primarily defined as behaviour aimed at benefiting others. Recent studies in evolutionary, social and positive psychology have highlighted that altruistic emotions and behaviours significantly contribute to wellbeing, happiness, health and longevity. However, few studies specifically focused on the concept of altruism, its experiential dimensions, cultural variants, meaning and related life domains. Hence, this study aims at exploring: a) how do people define altruism; b) perceived individual and social consequences of altruism; c) perceived difficulties in being altruistic; d) cultural influences on conceptions of altruism and related behaviours. The Altruism Questionnaire was specifically developed to address these issues. Qualitative data were collected among 119 adult participants (60 Indians and 59 Italians). Findings revealed that in both cultures altruism is perceived more than just as pro-social behaviour, emphasising it as human and social value along with its relational and psychological features. Improvement in relationships is reported as the most prominent benefit of being altruistic. Paradoxically, negative social evaluation such as criticism, isolation and misunderstanding is reported as the prominent difficulty. Influences of culture-specific factors were detected in the conceptualization and evaluation of altruism and altruistic behaviours, raising questions for assessment, intervention and further research.     

Reasoning About Collectively Accepted Group Beliefs

A proof-theoretical treatment of collectively accepted group beliefs is presented through a multi-agent sequent system for an axiomatization of the logic of acceptance. The system is based on a labelled sequent calculus for propositional multi-agent epistemic logic with labels that correspond to possible worlds and a notation for internalized accessibility relations between worlds. The system is contraction- and cut-free. Extensions of the basic system are considered, in particular with rules that allow the possibility of operative members or legislators. Completeness with respect to the underlying Kripke semantics follows from a general direct and uniform argument for labelled sequent calculi extended with mathematical rules for frame properties. As an example of the use of the calculus we present an analysis of the discursive dilemma.     

Varieties of Linear Calculi

A uniform calculus for linear logic is presented. The calculus has the form of a natural deduction system in sequent calculus style with general introduction and elimination rules. General elimination rules are motivated through an inversion principle, the dual form of which gives the general introduction rules. By restricting all the rules to their single-succedent versions, a uniform calculus for intuitionistic linear logic is obtained. The calculus encompasses both natural deduction and sequent calculus that are obtained as special instances from the uniform calculus. Other instances give all the invertibilities and partial invertibilities for the sequent calculus rules of linear logic. The calculus is normalizing and satisfies the subformula property for normal derivations.     

The Contribution of Job Happiness and Job Meaning to the Well-Being of Workers from Thriving and Failing Companies

In a time of global economic crisis, workers’ well-being is of paramount concern for both organizations and society at large. Conceptualizations within positive psychology distinguish between hedonic and eudaimonic well-being components, and call for the need to include them in an integrated perspective. Within this framework, the present study aimed at investigating the impact of situational uncertainty on eudaimonic and hedonic well-being, and the spillover effects of work into individuals’ lives. Data were collected from 85 Italian employees at a thriving insurance company and at a failing one. Participants were administered Job Content Questionnaire, Eudaimonic and Hedonic Happiness Investigation, Satisfaction with Life Scale, and Psychological Wellbeing Scales. Data were analyzed through hierarchical regression analyses. Concerning well-being at work, employees at the failing company reported higher job insecurity and lower job happiness compared to employees at the thriving company, while job meaning scores did not differ between groups. Concerning general well-being, an unexpected positive association was found between positive relations and situational uncertainty. A spillover effect of job happiness and meaning on life satisfaction, environmental mastery, and autonomy was also detected. In particular, a moderating effect of job meaning was identified, showing that attributing high importance to one’s job had wide affective consequences, spilling over to global life evaluations. Findings bring forward practical suggestions for well-being promotion, in terms of shifting domain importance (Wu Journal of Happiness Studies 10:37–47, 2009), and investing in multiple life areas (Sirgy and Wu Journal of Happiness Studies 10:183–196, 2009) for the promotion of a balanced life.     

The Church–Fitch knowability paradox in the light of structural proof theory

Anti-realist epistemic conceptions of truth imply what is called the knowability principle: All truths are possibly known. The principle can be formalized in a bimodal propositional logic, with an alethic modality ${\diamondsuit}$ and an epistemic modality ${\mathcal{K}}$ , by the axiom scheme ${A \supset \diamondsuit \mathcal{K} A}$ (KP). The use of classical logic and minimal assumptions about the two modalities lead to the paradoxical conclusion that all truths are known, ${A \supset \mathcal{K} A}$ (OP). A Gentzen-style reconstruction of the Church–Fitch paradox is presented following a labelled approach to sequent calculi. First, a cut-free system for classical (resp. intuitionistic) bimodal logic is introduced as the logical basis for the Church–Fitch paradox and the relationships between ${\mathcal {K}}$ and ${\diamondsuit}$ are taken into account. Afterwards, by exploiting the structural properties of the system, in particular cut elimination, the semantic frame conditions that correspond to KP are determined and added in the form of a block of nonlogical inference rules. Within this new system for classical and intuitionistic “knowability logic”, it is possible to give a satisfactory cut-free reconstruction of the Church–Fitch derivation and to confirm that OP is only classically derivable, but neither intuitionistically derivable nor intuitionistically admissible. Finally, it is shown that in classical knowability logic, the Church–Fitch derivation is nothing else but a fallacy and does not represent a real threat for anti-realism.