Epistemic modals in consequent place of indicative conditionals give rise to apparent counterexamples to Modus Ponens and Modus Tollens. Familiar assumptions of familiar truth conditional theories of modality facilitate a prima facie explanation—viz., that the target cases harbor epistemic modal equivocations. However, these explanations go too far. For they foster other predictions of equivoca...

This study discusses belief-change as the problem of deciding which previously-accepted belief, or premise, to abandon, when an inference from an initial belief set is subsequently contradicted. The data concern how "disbelieving" a previously-accepted conditional premise is realized as a particular modification to that premise. The types of revisions that are made are influenced by the kind of...

In this lecture we consider a logic as the set of its tautologies. The following definition captures the closure properties that the we expect from this set of tautologies: Definition 1 (Normal modal logic) A set L of formulas is called a normal modal logic if: 1. L contains all propositional tautologies 2. (p→ q)→ ( p→ q) ∈ L for all propositional letters p, q 3. A ∈ L, (A→ B) ∈ L implies B ∈ ...

In this work, an intuitionistic propositional logic with a Galois connection (IntGC) is introduced. In addition to the intuitionistic logic axioms and inference rule of modus ponens, the logic contains only two rules of inference mimicking the performance of Galois connections. Both Kripke-style and algebraic semantics are presented for IntGC, and IntGC is proved to be complete with respect to ...

Human answer patterns in psychological reasoning experiments systematically deviate from predictions of classical logic. When interactions between any artificial reasoning system and humans are necessary this difference can be useful in some cases and lead to problems in other cases. Hence, other approaches than classical logic might be better suited to capture human inference processes. Evalua...

In this paper, a theory T H based on combining type freeness with logic is introduced and is then used to build a theory of properties which is applied to determiners and quantiiers. It is well known that mixing type freeness and logic leads to contradictions. For example, by taking the following syntax of terms: t := xjx:tjt 1 t 2 j:t and applying the term x::xx to itself one gets a contradict...

In this paper, a theory T H based on combining type freeness with logic is introduced and is then used to build a theory of properties which is applied to determiners and quantiiers. It is well known that mixing type freeness and logic leads to contradictions. For example, by taking the following syntax of terms: t := xjx:tjt 1 t 2 j:t and applying the term x::xx to itself one gets a contradict...

Most merging operators are defined by semantics methods which have very high computational complexity. In order to have operators with a lower computational complexity, some merging operators defined in a syntactical way have be proposed. In this work we define some syntactical merging operators and exploring its rationality properties. To do that we constrain the belief bases to be sets of for...

The four dominant theories of reasoning from conditionals are translated into formal models: The theory of mental models (Johnson-Laird, P. N., & Byrne, R. M. J. (2002). Conditionals: a theory of meaning, pragmatics, and inference. Psychological Review, 109, 646-678), the suppositional theory (Evans, J. S. B. T., & Over, D. E. (2004). If. Oxford: Oxford University Press), a dual-process variant...

09h00 09h45 Zurab Janelidze Algebraic importance of “modus ponens” 09h50 10h20 Gareth Boxall NIP (Not the Independence Property) 10h25 10h55 James Gray Algebraic exponentiation 11h00 11h15 Tea/coffee Mathematics Tea Room 11h15 12h15 Alessandra Palmigiano Groupoid quantales beyond the étale setting 12h20 12h50 Willem Conradie Algorithmic canonicity and correspondence for (non-distributive) latti...