Logic and Logical Philosophy 

About: Logic and Logical Philosophy is an academic journal published by Uniwersytet Mikolaja Kopernika/Nicolaus Copernicus University. The journal publishes majorly in the area(s): Paraconsistent logic & Computer science. It has an ISSN identifier of 1425-3305. It is also open access. Over the lifetime, 500 publications have been published receiving 2403 citations.

Formal inconsistency and evolutionary databases

Abstract: This paper introduces new logical systems which axiomatize a formal representation of inconsistency (here taken to be equivalent to contradictoriness) in classical logic. We start from an intuitive semantical account of inconsistent data, fixing some basic requirements, and provide two distinct sound and complete axiomatics for such semantics, LFI1 and LFI2, as well as their first-order extensions, LFI1* and LFI2*, depending on which additional requirements are considered. These formal systems are examples of what we dub Logics of Formal Inconsistency (LFI) and form part of a much larger family of similar logics. We also show that there are translations from classical and paraconsistent first-order logics into LFI1* and LFI2*, and back. Hence, despite their status as subsystems of classical logic, LFI1* and LFI2* can codify any classical or paraconsistent reasoning.

A propositional calculus for inconsistent deductive systems

Abstract: Editorial note. Read at the meeting of section A, Societatis Scientiarum Torunensis, 19th March 1948. Published in Polish under the title “Rachunek zdan dla systemow dedukcyjnych sprzecznych”, in: Studia Societatis Scientiarum Torunensis, Sectio A, Vol. I, No. 5, Torun 1948, pp. 57–77. In original version the Polish notation was used. It is the second English version of this paper. The first one — translated by Olgierd Wojtasiewicz — was published under the title “Propositional calculus for contradictory deductive systems”, in Studia Logica, Vol. XXIV (1969), pp. 143–157. The present version is a small variation of the previous one. The chief difference is the change of the original Polish notation (done by A. Pietruszczak) into modern and standard one. For further Editorial Notes see Notes (denoted in the text by natural numbers) at the end of the paper.

Representing Concepts in Formal Ontologies: Compositionality vs. Typicality Effects"

Abstract: The problem of concept representation is relevant for many subfields of cognitive research, including psychology and philosophy, as well as artificial intelligence. In particular, in recent years it has received a great deal of attention within the field of knowledge representation, due to its relevance for both knowledge engineering as well as ontology-based technologies. However, the notion of a concept itself turns out to be highly disputed and problematic. In our opinion, one of the causes of this state of affairs is that the notion of a concept is, to some extent, heterogeneous, and encompasses different cognitive phenomena. This results in a strain between conflicting requirements, such as compositionality, on the one hand and the need to represent prototypical information on the other. In some ways artificial intelligence research shows traces of this situation. In this paper, we propose an analysis of this current state of affairs. Since it is our opinion that a mature methodology with which to approach knowledge representation and knowledge engineering should also take advantage of the empirical results of cognitive psychology concerning human abilities, we outline some proposals for concept representation in formal ontologies, which take into account suggestions from psychological research. Our basic assumption is that knowledge representation systems whose design takes into account evidence from experimental psychology (and which, therefore, are more similar to the human way of organizing and processing information) may therefore give better results in many applications (e.g. in the fields of information retrieval and semantic web).

Towards the unification of inconsistency handling mechanisms

Abstract: It is shown that the (flat) consequence relations defined from the Rescher-Manor Mechanism (that is: in terms of maximal consistent subsets of the premises) are all inconsistency-adaptive logics combined with a specific interpretation schema for the premises. Each of the adaptive logics is obtained by applying a suitable adaptive strategy to the paraconsistent logic CLuN. This result provides all those consequence relations with a (dynamic) proof theory and with a static (as well as a dynamic) semantics.

On the discussive conjunction in the propositional calculus for inconsistent deductive systems

Abstract: Editorial note. Read at the meeting of section A, Societatis Scientiarum Torunensis, 23th March 1949. Published in Polish under the title “O koniunkcji dyskusyjnej w rachunku zdan dla systemow dedukcyjnych sprzecznych”, in: Studia Societatis Scientiarum Torunensis, Sectio A, Vol. I, no. 8, Torun 1949, pp. 171–172.