Related papers: Admissibility in Positive Logics
This is the author's Ph.D. Thesis. It contains results from four years of research into realizability and categorical logic. The main subjects are the axiomatisation of realizable propositions, and a characterization of realizability…
This article will be a continuation of our research into self-justifying systems. It will introduce several new theorems and their applications. (One of these results will transform our previous infinite-sized self-verifying formalisms into…
In this paper, firstly, we determine the number of sublogics of variable inclusion of an arbitrary finitary logic L with partition function. Then, we investigate their position into the lattice of consequence relations over the language of…
Weighted gradual semantics provide an acceptability degree to each argument representing the strength of the argument, computed based on factors including background evidence for the argument, and taking into account interactions between…
In this paper, we introduce a general family of sequent-style calculi over the modal language and its fragments to capture the essence of all constructively acceptable systems. Calling these calculi \emph{constructive}, we show that any…
Conditional acceptability refers to how plausible a conditional statement is perceived to be. It plays an important role in communication and reasoning, as it influences how individuals interpret implications, assess arguments, and make…
Accounting for the epistemic contribution of deduction has been a pervasive problem for logicians interested in deduction, such as, among others, Jakko Hintikka. The problem arises because the conclusion validly deduced from a set of…
We revisit the application of different separability criteria by recourse to an exhaustive Monte Carlo exploration involving the pertinent state-space of pure and mixed states. The corresponding chain of implications of different criteria…
Plausible reasoning concerns situations whose inherent lack of precision is not quantified; that is, there are no degrees or levels of precision, and hence no use of numbers like probabilities. A hopefully comprehensive set of principles…
It is shown that admissible clauses and quasi-identities of quasivarieties generated by a single finite algebra, or equivalently, the quasiequational and universal theories of their free algebras on countably infinitely many generators, may…
Sub-sub-intuitionistic logic is obtained from intuitionistic logic by weakening the implication and removing distributivity. It can alternatively be viewed as conditional weak positive logic. We provide semantics for sub-sub-intuitionistic…
Building on our previous work on enriched regular logic, we introduce an enriched version of positive logic and relate it to enriched cone-injectivity classes and enriched accessible categories. To do this, we need a factorization system on…
Some large scale inference problems are considered based on using the relative belief ratio as a measure of statistical evidence. This approach is applied to the multiple testing problem. A particular application of this is concerned with…
Possibilistic logic offers a qualitative framework for representing pieces of information associated with levels of uncertainty of priority. The fusion of multiple sources information is discussed in this setting. Different classes of…
In many real-life situations that involve exchanges of arguments, individuals may differ on their assessment of which supports between the arguments are in fact justified, i.e., they put forward different support-relations. When confronted…
The paper presents a method for obtaining problems whose conclusions contain disjunctive propositions. These problems constitute a version of inverse problems with a given logical structure. The logical models in the groups of problems…
There are several contexts of non-monotonic reasoning where a priority between rules is established whose purpose is preventing conflicts. One formalism that has been widely employed for non-monotonic reasoning is the sceptical one known as…
We study abstract intermediate justification logics, that is arbitrary intermediate propositional logics extended with a subset of specific axioms of (classical) justification logics. For these, we introduce various semantics by combining…
Inductive theorem provers often diverge. This paper describes a simple critic, a computer program which monitors the construction of inductive proofs attempting to identify diverging proof attempts. Divergence is recognized by means of a…
In this note we prove that single-conclusion admissible rules of any proper axiomatic extension of the infnite valued Lukasiewicz logic are finitely based.