The paper concerns Grzegorczyk’s non-Fregean logics that are intended to be a formal representation of the equimeaning relation defined on descriptions. We argue that the main Grzegorczyk logics discussed in the literature are too strong and we propose a new logical system, \, which satisfies Grzegorczyk’s fundamental requirements. We present a sound and complete semantics for \ and we prove that it is decidable. Finally, we show that many non-classical logics are extensions of \, which makes it a generic non-Fregean (...) logic. (shrink)

We study the non-Fregean propositional logic with propositional quantifiers, denoted by $\mathsf{SCI}_{\mathsf{Q}}$. We prove that $\mathsf{SCI}_{\mathsf{Q}}$ does not have the finite model property and that it is undecidable. We also present examples of how to interpret in $\mathsf{SCI}_{\mathsf{Q}}$ various mathematical theories, such as the theory of groups, rings, and fields, and we characterize the spectra of $\mathsf{SCI}_{\mathsf{Q}}$-sentences. Finally, we present a translation of $\mathsf{SCI}_{\mathsf{Q}}$ into a classical two-sorted first-order logic, and we use the translation to prove some model-theoretic properties of (...) $\mathsf{SCI}_{\mathsf{Q}}$. (shrink)

This paper introduces Basic Intuitionistic Set Theory BIST, and investigates it as a first-order set theory extending the internal logic of elementary toposes. Given an elementary topos, together with the extra structure of a directed structural system of inclusions on the topos, a forcing-style interpretation of the language of first-order set theory in the topos is given, which conservatively extends the internal logic of the topos. This forcing interpretation applies to an arbitrary elementary topos, since any such is equivalent to (...) one carrying a dssi. We prove that the set theory BIST+Coll is sound and complete relative to forcing interpretations in toposes with natural numbers object . Furthermore, in the case that the structural system of inclusions is superdirected, the full Separation schema is modelled. We show that all cocomplete and realizability toposes can be endowed with such superdirected systems of inclusions.A large part of the paper is devoted to an alternative notion of category-theoretic model for BIST, which, following the general approach of Joyal and Moerdijkʼs Algebraic Set Theory, axiomatizes the structure possessed by categories of classes compatible with BIST. We prove soundness and completeness results for BIST relative to the class-category semantics. Furthermore, BIST+Coll is complete relative to the restricted collection of categories of classes given by categories of ideals over elementary toposes with nno and dssi. It is via this result that the completeness of the original forcing interpretation is obtained, since the internal logic of categories of ideals coincides with the forcing interpretation. (shrink)

This paper introduces Basic Intuitionistic Set Theory BIST, and investigates it as a first-order set theory extending the internal logic of elementary toposes. Given an elementary topos, together with the extra structure of a directed structural system of inclusions on the topos, a forcing-style interpretation of the language of first-order set theory in the topos is given, which conservatively extends the internal logic of the topos. This forcing interpretation applies to an arbitrary elementary topos, since any such is equivalent to (...) one carrying a dssi. We prove that the set theory BIST+Coll is sound and complete relative to forcing interpretations in toposes with natural numbers object. Furthermore, in the case that the structural system of inclusions is superdirected, the full Separation schema is modelled. We show that all cocomplete and realizability toposes can be endowed with such superdirected systems of inclusions.A large part of the paper is devoted to an alternative notion of category-theoretic model for BIST, which, following the general approach of Joyal and Moerdijkʼs Algebraic Set Theory, axiomatizes the structure possessed by categories of classes compatible with BIST. We prove soundness and completeness results for BIST relative to the class-category semantics. Furthermore, BIST+Coll is complete relative to the restricted collection of categories of classes given by categories of ideals over elementary toposes with nno and dssi. It is via this result that the completeness of the original forcing interpretation is obtained, since the internal logic of categories of ideals coincides with the forcing interpretation. (shrink)

We show that there are continuum many different extensions of SCI (the basic theory of non-Fregean propositional logic) that lie below WF (the Fregean extension) and are closed under substitution. Moreover, continuum many of them are independent from WB (the Boolean extension), continuum many lie above WB and are independent from WH (the Boolean extension with only two values for the equality relation), and only countably many lie between WH and WF.

We present two proof systems for first-order logic with identity and without function symbols. The first one is an extension of the Rasiowa-Sikorski system with the rules for identity. This system is a validity checker. The rules of this system preserve and reflect validity of disjunctions of their premises and conclusions. The other is a Tableau system, which is an unsatisfiability checker. Its rules preserve and reflect unsatisfiability of conjunctions of their premises and conclusions. We show that the two systems (...) are dual to each other. The duality is expressed in a formal way which enables us to define a transformation of proofs in one of the systems into the proofs of the other. (shrink)

We present a relational proof system in the style of dual tableaux for a multimodal propositional logic for order of magnitude qualitative reasoning to deal with relations of negligibility, non-closeness, and distance. This logic enables us to introduce the operation of qualitative sum for some classes of numbers. A relational formalization of the modal logic in question is introduced in this paper, i.e., we show how to construct a relational logic associated with the logic for order-of-magnitude reasoning and its dual (...) tableau system which is a validity checker for the modal logic. For that purpose, we define a validity preserving translation of the modal language into relational language. Then we prove that the system is sound and complete with respect to the relational logic defined as well as with respect to the logic for order of magnitude reasoning. Finally, we show that in fact relational dual tableau does more. It can be used for performing the four major reasoning tasks: verification of validity, proving entailment of a formula from a finite set of formulas, model checking, and verification of satisfaction of a formula in a finite model by a given object. (shrink)

The non-Fregean logic SCI is obtained from the classical sentential calculus by adding a new identity connective = and axioms which say ?a = ß' means ?a is identical to ß'. We present complete and sound proof system for SCI in the style of Rasiowa-Sikorski. It provides a natural deduction-style method of reasoning for the non-Fregean sentential logic SCI.

We study a new formal logic LD introduced by Prof. Grzegorczyk. The logic is based on so-called descriptive equivalence, corresponding to the idea of shared meaning rather than shared truth value. We construct a semantics for LD based on a new type of algebras and prove its soundness and completeness. We further show several examples of classical laws that hold for LD as well as laws that fail. Finally, we list a number of open problems. -/- .

Qualitative description of movements can be very important for representation and reasoning about dynamic systems which are complex in structure or whenever numerical data are incomplete or inaccessible. For this reason, we present a hybrid approach based on the combination of qualitative reasoning, quantitative data and logical methods. In this article, we introduce a new propositional dynamic logic QM for representation and reasoning with relative movements of objects. In this way, we can infer additional information about movements by using axioms (...) and the logic apparatus. We present a sound and complete deduction system in dual tableaux style for the logic QM. The system can be used for verification of validity of formulas of the logic in question. (shrink)

We show that there are continuum many different non-Fregean sentential logics that have adequate models. The proof is based on the construction of a special class of models of the power of the continuum.

Interval temporal logics provide both an insight into a nature of time and a framework for temporal reasoning in various areas of computer science. In this paper we present sound and complete relational proof systems in the style of dual tableaux for relational logics associated with modal logics of temporal intervals and we prove that the systems enable us to verify validity and entailment of these temporal logics. We show how to incorporate in the systems various relations between intervals and/or (...) various time orderings. (shrink)

It is known that various complexity-theoretical problems can be translated into some special spectra problems. Thus, questions about complexity classes are translated into questions about the expressive power of some languages. In this paper we investigate the spectra of some logics with Henkin quantifiers in the empty vocabulary.

We present a dual tableau system, RLK, which is itself a deterministic decision procedure verifying validity of K-formulas. The system is constructed in the framework of the original methodology of relational proof systems, determined only by axioms and inference rules, without any external techniques. Furthermore, we describe an implementation of the system in Prolog, and we show some of its advantages.

We introduce an Automatic Theorem Prover (ATP) of a dual tableau system for a relational logic for order of magnitude qualitative reasoning, which allows us to deal with relations such as negligibility, non-closeness and distance. Dual tableau systems are validity checkers that can serve as a tool for verification of a variety of tasks in order of magnitude reasoning, such as the use of qualitative sum of some classes of numbers. In the design of our ATP, we have introduced some (...) heuristics, such as the so called phantom variables, which improve the efficiency of the selection of variables used un the proof. (shrink)

In 2011, Andrzej Grzegorczyk formulated Logic of Descriptions, a new logical system in which the classical equivalence has been replaced with the descriptive equivalence. Two sentences are descriptively equivalent whenever they describe the same state of affairs. Grzegorczyk’s logic LD is built from the ground up by revising the axioms of classical propositional logic and rejecting those that do not correspond to the intended interpretation of the descriptive equivalence as the connective expressing equimeaning relations between sentences. Grzegorczyk’s last paper, which (...) introduced in detail philosophical motivations of LD and its axiomatization, has become an inspiration for investigating the properties of LD and its various modifications. In this paper we present the basics of Grzegorczyk’s logic LD and then we survey the recent results on LD that have shed light on mysterious properties of the Grzegorczyk’s descriptive equivalence connective. (shrink)

A new deduction system for deciding validity for the minimal decidable normal modal logic K is presented in this article. Modal logics could be very helpful in modelling dynamic and reactive systems such as bio-inspired systems and process algebras. In fact, recently the Connectionist Modal Logics has been presented, which combines the strengths of modal logics and neural networks. Thus, modal logic K is the basis for these approaches. Soundness, completeness and the fact that the system itself is a decision (...) procedure are proved in this article. The main advantages of this approach are: first, the system is deterministic, i.e. it generates one proof tree for a given formula; second, the system is a validity-checker, hence it generates a proof of a formula ; and third, the language of deduction and the language of a logic coincide. Some of these advantages are compared with other classical approaches. (shrink)

A non-Fregean framework aims to provide a formal tool for reasoning about semantic denotations of sentences and their interactions. Extending a logic to its non-Fregean version involves introducing a new connective $$\equiv $$ ≡ that allows to separate denotations of sentences from their logical values. Intuitively, $$\equiv $$ ≡ combines two sentences $$\varphi $$ φ and $$\psi $$ ψ into a true one whenever $$\varphi $$ φ and $$\psi $$ ψ have the same semantic correlates, describe the same situations, or (...) have the same content or meaning. The paper aims to compare non-Fregean paraconsistent Grzegorczyk’s logics (Logic of Descriptions $$\textsf{LD}$$ LD, Logic of Descriptions with Suszko’s Axioms $$\textsf{LDS}$$ LDS, Logic of Equimeaning $$\textsf{LDE}$$ LDE ) with non-Fregean versions of certain well-known paraconsistent logics (Jaśkowski’s Discussive Logic $$\textsf{D}_2$$ D 2, Logic of Paradox $$\textsf{LP}$$ LP, Logics of Formal Inconsistency $$\textsf{LFI}{1}$$ LFI 1 and $$\textsf{LFI}{2}$$ LFI 2 ). We prove that Grzegorczyk’s logics are either weaker than or incomparable to non-Fregean extensions of $$\textsf{LP}$$ LP, $$\textsf{LFI}{1}$$ LFI 1, $$\textsf{LFI}{2}$$ LFI 2. Furthermore, we show that non-Fregean extensions of $$\textsf{LP}$$ LP, $$\textsf{LFI}{1}$$ LFI 1, $$\textsf{LFI}{2}$$ LFI 2, and $$\textsf{D}_2$$ D 2 are more expressive than their original counterparts. Our results highlight that the non-Fregean connective $$\equiv $$ ≡ can serve as a tool for expressing various properties of the ontology underlying the logics under consideration. (shrink)

Logics of binary relations corresponding, among others, to the class RRA of representable relation algebras and the class FRA of full relation algebras are presented together with the proof systems in the style of dual tableaux. Next, the logics are extended with relational constants interpreted as point relations. Applications of these logics to reasoning in non-classical logics are recalled. An example is given of a dual tableau proof of an equation which is RRA-valid, while not RA-valid.

We present relational proof systems for the four groups of theories of spatial reasoning: contact relation algebras, Boolean algebras with a contact relation, lattice-based spatial theories, spatial theories based on a proximity relation.

Counselling acts consist in indicating useful activities, remedying human deficiencies. Counselling acts are guided by practical cognition. Since counselling activities are oriented towards the future, their crucial element is foresight. It is cognitive reflection foreseeing the implementation of counselling acts. Counselling acts are actualised in rhetorical and communicational context which is associated with persuasive delivery of counselling content. Belonging to the rhetorical canon, invention disposes of factors that influence the justifying formulation of advisory content. Invention factors introduce the anticipatory determinations (...) and concretisations of counselling content. At rhetorical level, inventive methodology plays anticipatory functions which are convergent with tasks of foresight in practical cognition. (shrink)

BackgroundIn this study, we analyze the association of social isolation in the first phase of the pandemic with perceived stress among residents of Poland and Italy with a look at how these populations adjust to and comply with implemented regulations, guidelines, and restrictions.Materials and MethodsInternet survey with Perceived Stress Scale (PSS-10) and questions regarding mobility patterns, attitude, and propensity to adjust toward the implemented measures and current health condition was made among Polish and Italian residents (Cronbach’s alpha 0.86 and 0.79, (...) respectively). The sample size was 7,108 (6,169 completed questionnaires in Poland and 939 in Italy).ResultsThe Polish group had a higher stress level than the Italian group (mean PSS-10 total score 22,14 vs 17,01, respectively;p< 0.01). There was a greater prevalence of chronic diseases among Polish respondents. Italian subjects expressed more concern about their health, as well as about their future employment. Italian subjects did not comply with suggested restrictions as much as Polish subjects and were less eager to restrain from their usual activities (social, physical, and religious), which were more often perceived as “most needed matters” in Italian than in Polish residents.ConclusionHigher activity level was found to be correlated with lower perceived stress, but the causality is unclear. Difference in adherence to restrictions between Polish and Italian residents suggests that introducing similar lockdown policies worldwide may not be as beneficial as expected. However, due to the applied method of convenience sampling and uneven study groups, one should be careful with generalizing these results. (shrink)

In this paper, we discuss the processes of racialisation on the example of biomedical research. We argue that applying the concept of racialisation in biomedical research can be much more precise, informative and suitable than currently used categories, such as race and ethnicity. For this purpose, we construct a model of the different processes affecting and co-shaping the racialisation of an individual, and consider these in relation to biomedical research, particularly to studies on hypertension. We finish with a discussion on (...) the potential application of our proposition to institutional guidelines on the use of racial categories in biomedical research. (shrink)

The doctrine of paṭicca samuppāda or dependent co-arising is fundamental to Buddhist ethics. In this vision of radical relativity, reality appears as an interdependent process wherein change and choice, doer and deed, person and community are mutually causative. Morality is grounded in this interdependence, as in the corrollary Buddhist views of anattā and karma. Consequently it reveals a reciprocal dynamic between personal and social transformation, expressed in Buddhist scripture and illustrated in a contemporary Buddhist movement in Sri Lanka.

A CHOICE Outstanding Academic Title 2012! Contemporary picturebooks open up spaces for philosophical dialogues between people of all ages. As works of art, picturebooks offer unique opportunities to explore ideas and to create meaning collaboratively. This book considers censorship of certain well-known picturebooks, challenging the assumptions on which this censorship is based. Through a lively exploration of children's responses to these same picturebooks the authors paint a way of working philosophically based on respectful listening and creative and authentic interactions, rather (...) than scripted lessons. This dialogical process challenges much current practice in education. The authors propose that a courageous and critical practice of listening is central to the facilitation of mutually educative dialogue. This book will be of interest to scholars and students of education studies, philosophy of education, literacy teaching and learning, children's literature, childhood and pedagogy. (shrink)

A blueprint for social change showing how we can reverse the destructive attitudes that threaten our world.

Life typically becomes an object of reflection when it is seen to be under threat. In particular, humans have a tendency to engage in thinking about life (instead of just continuing to live it) when being confronted with the prospect of death: be it the death of individuals due to illness, accident or old age; the death of whole ethnic or national groups in wars and other forms of armed conflict; but also of whole populations, be they human or nonhuman. (...) Even though Minimal Ethics for the Anthropocene is first and foremost concerned with life--understood as both a biological and social phenomenon--it is the narrative about the impending death of the human population (i.e., about the extinction of the human species), that provides a context for its argument. "Anthropocene" names a geo-historical period in which humans are said to have become the biggest threat to life on earth. However, rather than as a scientific descriptor, the term serves here primarily as an ethical injunction to think critically about human and nonhuman agency in the universe. Restrained in tone yet ambitious in scope, the book takes some steps towards outlining a minimal ethics thought on a universal scale. The task of such minimal ethics is to consider how humans can assume responsibility for various occurrences in the universe, across different scales, and how they can respond to the tangled mesh of connections and relations unfolding in it. Its goal is not so much to tell us how to live but rather to allow us to rethink "life" and what we can do with it, in whatever time we have left. The book embraces a speculative mode of thinking that is more akin to the artist's method; it also includes a photographic project by the author."--Publisher's description. (shrink)

An imagined retrospective of apocalyptic art.

Heidegger and ethics is a contentious conjunction of terms. Martin Heidegger himself rejected the notion of ethics, while his endorsement of Nazism is widely seen as unethical. This major study examines the complex and controversial issues involved in bringing Heidegger and ethics together. Working backwards through his work, from his 1964 claim that philosophy has been completed to his first major book, Being and Time, Joanna Hodge questions Heidegger's denial that his inquiries were concerned with ethics. She discovers a (...) form of ethics in Heidegger's thinking which elucidates his important distinction between metaphysics and philosophy. Opposing many contemporary views, Hodge proposes that ethics can be retrieved and questions the relation between ethics and metaphysics that Heidegger made so pervasive. (shrink)

The question of whether AI systems such as robots can or should be afforded moral agency or patiency is not one amenable either to discovery or simple reasoning, because we as societies constantly reconstruct our artefacts, including our ethical systems. Consequently, the place of AI systems in society is a matter of normative, not descriptive ethics. Here I start from a functionalist assumption, that ethics is the set of behaviour that maintains a society. This assumption allows me to exploit the (...) theoretical biology of sociality and autonomy to explain our moral intuitions. From this grounding I extend to consider possible ethics for maintaining either human- or of artefact-centred societies. I conclude that while constructing AI systems as either moral agents or patients is possible, neither is desirable. In particular, I argue that we are unlikely to construct a coherent ethics in which it it is ethical to afford AI moral subjectivity. We are therefore obliged not to build AI we are obliged to. (shrink)

Joanna Demers argues that Houellebecqs apocalypse can be understood as a system analogous to Hegels, and interrogates the ethics of such a system.

In this article I examine how a ‘private’, inside story was constructed through an extended news interview drawing on models of both the experiential and the accountable broadcast interview. The analysis, based on aspects of adjacency sequencing, question/ response design, and narrative organization, explores the ways in which a personal account is elicited about an event that had been highly prominent in the news. However, I also look at how ‘accountability’ emerges as an issue during the interview, and on how (...) the tensions between these two types of interview are played out in its design and subsequent editing. Although the interview displays many of the characteristics identified by Montgomery as ‘experiential’, where the interviewee is positioned as ‘one of us’, with knowledge and experience of an event she is not to be held accountable for as a result of her high profile in the news coverage of the Iranian hostage crisis, Faye Turney had already become a public figure during the time she was held in Iran. Furthermore, she had already been positioned by the media as accountable for some of her actions during her captivity. I show that the personal dimensions of the interview as interaction are framed by the interview as documentary, thus producing a hybrid form in which both the experiential and the accountable can be managed. (shrink)