Choice revision Abstract Choice revision is a sort of non-prioritized multiple revision, in which the agent partially accepts the new information represented by a set of sentences. We investigate the construction of choice revision based on a new approach to belief change called descriptor revision. We prove that each of two variants of choice revision based on such construction is axiomatically characterized with a set of plausible postulates, assuming that the object language is finite. Furthermore, we introduce an alternative modelling for choice revision, which is based on a type of relation on sets of sentences, named multiple believability relation. We show without assuming a finite language that choice revision constructed from such relations is axiomatically characterized with the same sets of postulates that we proposed for the choice revision based on descriptor revision, whenever the relations satisfy certain rationality conditions.

Inductive Reasoning in Social Choice Theory Abstract The usual procedure in the theory of social choice consists in postulating some desirable properties which an aggregation procedure should verify and derive from them the features of a corresponding social choice function and the outcomes that arise at each possible profile of preferences. In this paper we invert this line of reasoning and try to infer, up from what we call social situations (each one consisting of a profile and the associated social ordering) the criteria verified in the implicit aggregation procedure. This inference process, which extracts intensional from extensional information can be seen as an exercise in “qualitative statistics”.

Lewis’ Triviality for Quasi Probabilities Abstract According to Stalnaker’s Thesis (S), the probability of a conditional is the conditional probability. Under some mild conditions, the thesis trivialises probabilities and conditionals, as initially shown by David Lewis. This article asks the following question: does (S) still lead to triviality, if the probability function in (S) is replaced by a probability-like function? The article considers plausibility functions, in the sense of Friedman and Halpern, which additionally mimic probabilistic additivity and conditionalisation. These quasi probabilities comprise Friedman–Halpern’s conditional plausibility spaces, as well as other known representations of conditional doxastic states. The paper proves Lewis’ triviality for quasi probabilities and discusses how this has implications for three other prominent strategies to avoid Lewis’ triviality: (1) Adams’ thesis, where the probability function on the left in (S) is replaced by a probability-like function, (2) abandoning conditionalisation, where probability conditionalisation on the right in (S) is replaced by another propositional update procedure and (3) the approximation thesis, where equality in (S) is replaced by approximation. The paper also shows that Lewis’ triviality result is really about ‘additiveness’ and ‘conditionality’.

Translation Invariance and Miller’s Weather Example Abstract In his 1974 paper “Popper’s qualitative theory of verisimilitude” published in the British Journal for the Philosophy of Science David Miller gave his so called ‘Weather Example’ to argue that the Hamming distance between constituents is flawed as a measure of proximity to truth since the former is not, unlike the latter, translation invariant. In this present paper we generalise David Miller’s Weather Example in both the unary and polyadic cases, characterising precisely which permutations of constituents/atoms can be effected by translations. In turn this suggests a meta-principle of the rational assignment of subjective probabilities, that rational principles should be preserved under translations, which we formalise and give a particular characterisation of in the context of Unary Pure Inductive Logic.

The Class of All Natural Implicative Expansions of Kleene’s Strong Logic Functionally Equivalent to Łkasiewicz’s 3-Valued Logic Ł3 Abstract We consider the logics determined by the set of all natural implicative expansions of Kleene’s strong 3-valued matrix (with both only one and two designated values) and select the class of all logics functionally equivalent to Łukasiewicz’s 3-valued logic Ł3. The concept of a “natural implicative matrix” is based upon the notion of a “natural conditional” defined in Tomova (Rep Math Log 47:173–182, 2012).

A Note on the Issue of Cohesiveness in Canonical Models Abstract In their presentation of canonical models for normal systems of modal logic, Hughes and Cresswell observe that some of these models are based on a frame which can be also thought of as a collection of two or more isolated frames; they call such frames ‘non-cohesive’. The problem of checking whether the canonical model of a given system is cohesive is still rather unexplored and no general decision procedure is available. The main contribution of this article consists in introducing a method which is sufficient to show that canonical models of some relevant classes of normal monomodal and bimodal systems are always non-cohesive.

The Thin Red Line, Molinism, and the Flow of Time Abstract In addressing the problem of the (in)compatibility of divine foreknowledge and human freedom, philosophers of religion encounter problems regarding the metaphysics and structure of time. Some models of temporal logic developed for completely independent reasons have proved especially appropriate for representing the temporal structure of the world as Molinism conceives it. In particular, some models of the Thin Red Line ( \(\mathsf {TRL}\) ) seem to imply that conditionals of freedom are true or false, as Molinists maintain. Noting the resemblance between Molinism and \(\mathsf {TRL}\) models, Restall (Molinism and the thin red line. In: Perszyk K (ed) Molinism: the contemporary debate, pp 227–239, 2011) has advanced some criticisms of Molinism that have also been leveled against \(\mathsf {TRL}\) models. In particular, Restall believes that the implication \(p \rightarrow \mathbf {HF}p\) is not true in \(\mathsf {TRL}\) models. Because Molinists must also accept that this implication is not true, this is a problem for them. We will show that Restall’s criticism is wide of the mark. Firstly, it will be demonstrated that in many open future models (not just \(\mathsf {TRL}\) ) the implication \(p \rightarrow \mathbf {HF}p\) is invalid. Secondly, while it is possible to account for this implication, some modifications are required in respect of the branching time semantics. In proposing one such modification, we show that this new semantics can be adopted by advocates of the \(\mathsf {TRL}\) and, as a consequence, by Molinists as well. We conclude that the principle stated by Restall is either a problem for many open future models (not just for Molinists) or can be accounted for by these models and so is not a problem for Molinists either.

Group Conformity in Social Networks Abstract Diffusion in social networks is a result of agents’ natural desires to conform to the behavioral patterns of their peers. In this article we show that the recently proposed “propositional opinion diffusion model” could be used to model an agent’s conformity to different social groups that the same agent might belong to, rather than conformity to the society as whole. The main technical contribution of this article is a sound and complete logical system describing the properties of the influence relation in this model. The logical system is an extension of Armstrong’s axioms from database theory by one new axiom that captures the topological structure of the network.

On Relation Between Linear Temporal Logic and Quantum Finite Automata Abstract Linear temporal logic is a widely used method for verification of model checking and expressing the system specifications. The relationship between theory of automata and logic had a great influence in the computer science. Investigation of the relationship between quantum finite automata and linear temporal logic is a natural goal. In this paper, we present a construction of quantum finite automata on finite words from linear-time temporal logic formulas. Further, the relation between quantum finite automata and linear temporal logic is explored in terms of language recognition and acceptance probability. We have shown that the class of languages accepted by quantum finite automata are definable in linear temporal logic, except for measure-once one-way quantum finite automata.

Residual Contraction Abstract In this paper, we propose and axiomatically characterize residual contractions, a new kind of contraction operators for belief bases. We establish that the class of partial meet contractions is a strict subclass of the class of residual contractions. We identify an extra condition that may be added to the definition of residual contractions, which is such that the class of residual contractions that satisfy it coincides with the class of partial meet contractions. We investigate the interrelations in the sense of (strict) inclusion among the class of residual contractions and other classes of well known contraction operators for belief bases.