I argue that the role played by infons in the kind of mathematical theory of information being developed by several workers affiliated to CSLI is analogous to that of the various number systems in mathematics. In particular, I present a mathematical construction of infons in terms of representations and informational equivalences between them. The main theme of the paper arose from an electronic mail exchange with Pat Hayes of Xeroxparc. The exposition derives from a talk I gave at theTheories of (...) Partial Information conference held at the University of Texas at Austin, January 1990. (shrink)

Primal infon logic was introduced in 2009 in connection with access control. In addition to traditional logic constructs, it contains unary connectives p said indispensable in the intended access control applications. Propositional primal infon logic is decidable in linear time, yet suffices for many common access control scenarios. The most obvious limitation on its expressivity is the failure of the transitivity law for implication: \$$ \to \$$ and \$$ \to \$$ do not necessarily yield \$$ \to \$$. Here (...) we introduce and investigate equiexpressive extensions TPIL and TPIL* of propositional primal infon logic as well as their quote-free fragments TPIL0 and TPIL0* respectively. We prove the subformula property for TPIL0* and a similar property for TPIL*; we define Kripke models for the four logics and prove the corresponding soundness-and-completeness theorems; we show that, in all these logics, satisfiable formulas have small models; but our main result is a quadratic-time derivation algorithm for TPIL*. (shrink)

Autor (2020) desenvolveu duas semânticas informacionais para a Lógica Sentencial Clássica, decorrentes da utilização de formais normais. A abordagem informacional em questão utiliza unidades mínimas de informação (infons) para realizar o trabalho lógico. Neste artigo, expandiremos a aplicação da abordagem informacional às lógicas sentenciais polivalentes finitas mediante um procedimento dedicado à extração de unidades mínimas de informação (infons). Tal procedimento decorre do trabalho com tablôs semânticos para Lógicas Sentenciais Polivalentes Finitas desenvolvido por Carnielli (1982).

Formulações da validade dedutiva clássica costumam recorrer explicitamente a modalidades: por exemplo, um argumento é classicamente dedutivamente válido se, e somente se, necessariamente se as premissas forem verdadeiras, a conclusão também é verdadeira. Não é possível abolir completamente esse apelo ao discurso modal, porque a lógica clássica é o domínio das possibilidades. Não obstante, pode-se, por intermédio de uma semântica informacional, evitar que o usuário da lógica clássica tenha de manipular modalidades, ainda que elas estejam, de algum modo, imbricadas nos (...) infons – unidades mínimas de informação. A partir do trabalho pioneiro de Carnap e de Bar-Hillel, apresentarei duas semânticas informacionais: uma delas diretamente relacionada a mundos possíveis, e a outra relacionada aos duais de mundos possíveis. (shrink)

Intuitively Austinian propositions are propositions that tell us something about a situation In this paper we will consider Austinian propositions and the associated notion that situations support infons which are to be found in situation theory and situation semantics We will try to tease out the consequences of taking the Austinian approach advocated in situation semantics as opposed to a very similar approach originally proposed by Davidson That is that event predicates where events are to be generally conceived so as (...) to be more like the notion of sit uation i e including states and processes are taken to have an argument position for an event We will do this comparison with respect to an area of data that was part of the original motivation for situation semantics naked in nitive perception complements see Barwise and Perry We will see that negative descriptions of events are one area where the Austinian and Davidsonian approaches make dif ferent predictions and at the end of the paper we will brie y consider negative event descriptions more generally with particular reference to the DRT analysis based on a Davidsonian approach as exempli ed by Amsili and Le Draoulec this volume.. (shrink)

Many philosophers of language and mind have recognized the existence of two distinct kinds of content assigned to our linguistic and mental representations. Thus following Kaplan , the character is the linguistic meaning of an expression-type, while the content is the propositional content expressed by a token of that expression in a context. Perry applied Kaplan's distinction in the analysis of belief: the proposition p is what a subject S believes, and the belief state is that in virtue of which (...) S believes p; where belief states are individuated by the characters of the sentences that S is disposed to assert. And Barwise and Etchemendy distinguished between the infon and the Austinian proposition, where the former is the content to be evaluated with respect to a situation, and the latter is the complete content, including both the infon and the situation.The possibility of operating with two kinds of content arises when a distinction is drawn between two kinds of context-dependence. Since Kaplan, we are familiar with the idea that context determines both the content of a sentence containing an indexical and the circumstance with respect to which that content is evaluated. So, truth values depend on the context of utterance and on the circumstance of evaluation. Whether an utterance of ‘I feel elated’ is true or false depends on both which proposition is expressed, i.e. who the speaker is, and on whether that proposition is evaluated with respect to the time and world of the context. Variation in either factor makes for a potential change in truth value. Also well-known is Kaplan's idea that contents have relative truth conditions: they are true with respect to world-time-place triples. The temporal operator ‘now’ in ‘I feel elated now’ specifies the time with respect to which the proposition …. (shrink)

In this paper, we define a first-order logic CFʹ with strong negation and bounded static quantifiers, which is a variant of Thomason's logic CF. For the logic CFʹ, the usual Kripke formal semantics is defined based on situations, and a sound and complete axiomatic system is established based on the axiomatic systems of constructive logics with strong negation and Thomason's completeness proof techniques. With the use of bounded quantifiers, CFʹ allows the domain of quantification to be empty and allows for (...) nondenoting constants. CFʹ is intended as a fragment of a logic for situation theory. Thus the connection between CFʹ and infon logic is discussed. (shrink)