The logic of fast and slow thinking

Anthia Solaki’s research is funded by the Netherlands Organisation for Scientific Research (NWO) ‘PhD in the Humanities’ programme, Grant No. 322-20-018. Franz Berto’s research is funded by the European Research Council (ERC CoG) ‘The Logic of Conceivability’ Project, Grant No. 681404.We present a framework for epistemic logic, modeling the logical aspects of System 1 (“fast”) and System 2 (“slow”) cognitive processes, as per dual process theories of reasoning. The framework combines non-normal worlds semantics with the techniques of Dynamic Epistemic Logic. It models non-logically-omniscient, but moderately rational agents: their System 1 makes fast sense of incoming information by integrating it on the basis of their background knowledge and beliefs. Their System 2 allows them to slowly, step-wise unpack some of the logical consequences of such knowledge and beliefs, by paying a cognitive cost. The framework is applied to three instances of limited rationality, widely discussed in cognitive psychology: Stereotypical Thinking, the Framing Effect, and the Anchoring Effect.Publisher PDFPeer reviewe

Dynamic epistemic logics for abstract argumentation

AbstractThis paper introduces a multi-agent dynamic epistemic logic for abstract argumentation. Its main motivation is to build a general framework for modelling the dynamics of a debate, which entails reasoning about goals, beliefs, as well as policies of communication and information update by the participants. After locating our proposal and introducing the relevant tools from abstract argumentation, we proceed to build a three-tiered logical approach. At the first level, we use the language of propositional logic to encode states of a multi-agent debate. This language allows to specify which arguments any agent is aware of, as well as their subjective justification status. We then extend our language and semantics to that of epistemic logic, in order to model individuals' beliefs about the state of the debate, which includes uncertainty about the information available to others. As a third step, we introduce a framework of dynamic epistemic logic and its semantics, which is essentially based on so-called event models with factual change. We provide completeness results for a number of systems and show how existing formalisms for argumentation dynamics and unquantified uncertainty can be reduced to their semantics. The resulting framework allows reasoning about subtle epistemic and argumentative updates—such as the effects of different levels of trust in a source—and more in general about the epistemic dimensions of strategic communication

Per una caratterizzazione formale della conoscenza di individui concreti. Un'analisi del problema di onniscienza logica

Questa tesi intende proporre una caratterizzazione formale della conoscenza di individui concreti, vale a dire di agenti con risorse computazionali limitate. Si mostra che le logiche epistemiche classiche non sono adeguate a raggiungere questo scopo: esse considerano il ragionamento di agenti deduttivamente onniscienti. Un'analisi storico-filosofica porta a identificare la causa del problema dell'onniscienza nel principio di analiticità della logica. Tuttavia quest’ultimo è incompatibile con la probabile intrattabilità del calcolo proposizionale classico. Si esamina la recente proposta delle logiche booleane a profondità limitata di D'Agostino e Floridi che distinguono tra inferenze proposizionali analitiche e sintetiche a priori, sulla base delle risorse computazionali necessarie alla deduzione. Si propone quindi una versione modale di quest'approccio: la logica epistemica a profondità limitata caratterizza la conoscenza di individui concreti dal momento che assume soltanto che i suoi agenti conoscano le conseguenze analitiche di ciò che sanno. Infine, si suggerisce un'applicazione di questa caratterizzazione degli agenti concreti al contesto sociale dell'aggregazione di giudizi

The principle of analyticity of logic : a philosophical and formal Perspective

The subject of the present work is the principle of analyticity of logic. In order for the question \u2018Is logic analytic?\u2019 to make sense and before trying to \ufb01nd an answer to this problem, it is obviously necessary to specify two preliminary issues, namely, the meaning of the term \u2018analytic\u2019 and the meaning of the term \u2018logic\u2019. The former issue is somehow justi\ufb01ed and expected: after all, analyticity represents one of the philosophical concepts par excellence and, as such, it has been at the core of a lively debate throughout the history of the discipline. But, despite possible appearances to the contrary, the second issue is probably more decisive than the former in determining the answer to the initial question: both the contents and the philosophical conceptions of logic play a fundamental role in the study of the epistemological status of this discipline. We could even say that the clari\ufb01cation of the concepts of analyticity and of logic constitutes in itself the decision on the analyticity of logic. This thesis studies the principle of analyticity of logic through two di\ufb00erent, but related, methodologies, which individuate the two main parts of the work: the former o\ufb00ers a historical and philosophical reconstruction of the problem; the latter proposes two formal characterizations of the analytic-synthetic distinction. The reconstruction of the \ufb01rst part does not presume to be exhaustive and is restricted to the theories of the following philosophers: Kant, Bolzano, Frege and Hintikka. The material has been chosen according to the following criteria. First, this work aims at showing the \u2018historical\u2019 nature of the principle of analyticity of logic, which has a certain genealogy and a precise starting point. Although after the Vienna Circle this tenet has been taken for granted, there are many and signi\ufb01cant conceptions that criticize it. Theories holding that logic is either not analytic or synthetic are the main characters of our reconstruction. This explains, for example, why we have dedicated great attention to Bolzano, while leaving little margin to the logical empiricist movement, despite the fact that analyticity is probably more fundamental for the latter\u2019s thought than for the former\u2019s philosophical construction. As a result of this choice, theories of meaning and their connection to analyticity are completely overlooked, since they belong to the logical empiricists\u2019 interpretation of the analytic-synthetic distinction. In other words, the principle of analyticity of logic and the philosophers arguing for it are taken as a critical target, but the true focus is on the varieties of reactions against them. [...