scholarly journals A propositional p-adic probability logic

2010 ◽  
Vol 87 (101) ◽  
pp. 75-83 ◽  
Author(s):  
Milos Milosevic
Keyword(s):  
Axiom System ◽  
Propositional Formula ◽  
Kripke Models ◽  
Probability Logic ◽  
Intended Meaning ◽  
Logical Language

We present the p-adic probability logic LpPP based on the paper [5] by A. Khrennikov et al. The logical language contains formulas such as P=s(?) with the intended meaning 'the probability of ? is equal to s', where ? is a propositional formula. We introduce a class of Kripke-like models that combine properties of the usual Kripke models and finitely additive p-adic probabilities. We propose an infinitary axiom system and prove that it is sound and strongly complete with respect to the considered class of models. In the paper the terms finitary and infinitary concern the meta language only, i.e., the logical language is countable, formulas are finite, while only proofs are allowed to be infinite. We analyze decidability of LpPP and provide a procedure which decides satisfiability of a given probability formula.

scholarly journals A logic with higher order conditional probabilities

2007 ◽  
pp. 141-154 ◽  
Author(s):  
Zoran Ognjanovic ◽  
Nebojsa Ikodinovic
Keyword(s):  
Conditional Probability ◽  
Probability Space ◽  
Possible Worlds ◽  
Axiomatic System ◽  
Probability Logic ◽  
Conditional Probabilities ◽  
Unconditional Probability ◽  
Possible World ◽  
Intended Meaning ◽  
Probability Operators

We investigate probability logic with the conditional probability operators This logic, denoted LCP, allows making statements such as: P?s?, CP?s(? | ?) CP?0(? | ?) with the intended meaning "the probability of ? is at least s" "the conditional probability of ? given ? is at least s", "the conditional probability of ? given ? at most 0". A possible-world approach is proposed to give semantics to such formulas. Every world of a given set of worlds is equipped with a probability space and conditional probability is derived in the usual way: P(? | ?) = P(?^?)/P(?), P(?) > 0, by the (unconditional) probability measure that is defined on an algebra of subsets of possible worlds. Infinitary axiomatic system for our logic which is sound and complete with respect to the mentioned class of models is given. Decidability of the presented logic is proved.

scholarly journals A first-order conditional probability logic with iterations

2013 ◽  
Vol 93 (107) ◽  
pp. 19-27 ◽  
Author(s):  
Milos Milosevic ◽  
Zoran Ognjanovic
Keyword(s):  
Conditional Probability ◽  
Completeness Theorem ◽  
Axiomatic System ◽  
Probability Logic ◽  
Intended Meaning ◽  
First Order

We investigate a first-order conditional probability logic with equality, which is, up to our knowledge, the first treatise of such logic. The logic, denoted LFPOIC=, allows making statements such as: CP?s(?, ?), and CP?s(?, ?), with the intended meaning that the conditional probability of ? given ? is at least (at most) s. The corresponding syntax, semantic, and axiomatic system are introduced, and Extended completeness theorem is proven.

QUALITATIVE MODALITIES

1996 ◽  
Vol 04 (01) ◽  
pp. 45-59 ◽  
Author(s):  
WIEBE VAN DER HOEK
Keyword(s):  
Finite Additivity ◽  
Modal Operator ◽  
Countable Additivity ◽  
Intended Meaning ◽  
Finite Models ◽  
Logical Language ◽  
Binary Operator ◽  
Kripke Structures

We add a binary operator ≥ to the logical language, with intended meaning of φ<ψ: ‘φ is at least as likely, probable, or trustworthy, as ψ’. The operator ≥ is interpreted on Kripke structures, making it possible to define the standard necessity operator □ in terms of ≥. The operator ≥ provides us with an intermediate for the K-axiom, in the sense that we have both □(p→q)→(q≥p) and (q≥p)→(□p→□q). We discuss two semantics for this binary modal operator. It turns out that, as shown by Gärdenfors and Segerberg, ≥ is not only too weak to distinguish finite models from infinite ones or to distinguish countable additivity from finite additivity, ≥ also cannot distinguish sophisticated ways of assigning exact probabilities to events (‘measuring’) from the conceptually simpler task of just counting them.

scholarly journals Inference rules for probability logic

2016 ◽  
Vol 100 (114) ◽  
pp. 77-86 ◽  
Author(s):  
Marija Boricic
Keyword(s):  
Twentieth Century ◽  
Inference Rules ◽  
Probability Logic ◽  
Elimination Rule ◽  
Probability Models ◽  
Intended Meaning ◽  
Deductive Systems ◽  
Traditional Proof

Gentzen?s and Prawitz?s approach to deductive systems, and Carnap?s and Popper?s treatment of probability in logic were two fruitful ideas of logic in the mid-twentieth century. By combining these two concepts, the notion of sentence probability, and the deduction relation formalized by means of inference rules, we introduce a system of inference rules based on the traditional proof-theoretic principles enabling to work with each form of probabilized propositional formulae. Namely, for each propositional connective, we define at least one introduction and one elimination rule, over the formulae of the form A[a,b] with the intended meaning that ?the probability c of truthfulness of a sentence A belongs to the interval [a,b] ?[0,1]?. It is shown that our system is sound and complete with respect to the Carnap-Poper-type probability models.

scholarly journals MODEL-THEORETIC CHARACTERIZATION OF INTUITIONISTIC PROPOSITIONAL FORMULAS

2013 ◽  
Vol 6 (2) ◽  
pp. 348-365 ◽  
Author(s):  
GRIGORY K. OLKHOVIKOV
Keyword(s):  
Propositional Formula ◽  
Kripke Models ◽  
First Order ◽  
Theoretic Characterization

AbstractNotions of k-asimulation and asimulation are introduced as asymmetric counterparts to k-bisimulation and bisimulation, respectively. It is proved that a first-order formula is equivalent to a standard translation of an intuitionistic propositional formula iff it is invariant with respect to k-asimulations for some k, and then that a first-order formula is equivalent to a standard translation of an intuitionistic propositional formula iff it is invariant with respect to asimulations. Finally, it is proved that a first-order formula is equivalent to a standard translation of an intuitionistic propositional formula over the class of intuitionistic Kripke models iff it is invariant with respect to asimulations between intuitionistic models.

scholarly journals Complex valued probability logics

2014 ◽  
Vol 95 (109) ◽  
pp. 73-86 ◽  
Author(s):  
Angelina Ilic-Stepic ◽  
Zoran Ognjanovic
Keyword(s):  
Propositional Logic ◽  
Linear Inequalities ◽  
Satisfiability Problem ◽  
Propositional Formula ◽  
Classical Propositional Logic ◽  
Intended Meaning ◽  
Complex Ball ◽  
Axiom Systems ◽  
Complex Valued

We present two complex valued probabilistic logics, LCOMPB and LCOMPS, which extend classical propositional logic. In LCOMPB one can express formulas of the form Bz,?? meaning that the probability of ? is in the complex ball with the center z and the radius ?, while in LCOMPS one can make statements of the form Sz,?? with the intended meaning - the probability of propositional formula ? is in the complex square with the center z and the side 2?. The corresponding strongly complete axiom systems are provided. Decidability of the logics are proved by reducing the satisfiability problem for LCOMPB (LCOMPS) to the problem of solving systems of quadratic (linear) inequalities.

Aux frontières de l'expérience esthétique: le grotesque baudelairien

2019 ◽  
Vol 58 (2) ◽  
pp. 237-248
Author(s):  
Julien Weber
Keyword(s):  
Aesthetic Experience ◽  
A Priori ◽  
Intended Meaning ◽  
The Grotesque

This article is about the grotesque in Baudelaire. While Baudelaire's famous essay on laughter plays an important role in contemporary theories of grotesque aesthetics, his own poetic production is often left aside. In this article, I discuss how the grotesque manifests itself in works by Baudelaire that seem a priori irrelevant because of their ostensible use of ‘comique significatif’, a sort of antithesis of the grotesque. Through a discussion of Pauvre Belgique! And ‘Le Chien et le Flacon’, I argue that the baudelairian grotesque most powerfully intervenes in the mode of a distortion of the intended meaning, which leads me to distinguish its reading from a properly ‘aesthetic’ experience.

Directive Speech Act Seen on Family 2.0 Drama Script Written by Walter Wykes

2018 ◽  
Vol 8 (2) ◽  
Author(s):  
Evi Jovita Putri
Keyword(s):  
Speech Acts ◽  
Speech Act ◽  
Declarative Sentence ◽  
Pragmatic Approach ◽  
Intended Meaning ◽  
Descriptive Research ◽  
Directive Speech Acts ◽  
Directive Speech

<p>The research entitled Directive Speech Act Seen on Family 2.0 Drama Script Written by Walter Wykes purposes to describe and uncover the types of form and intended meaning of directive speech act on that drama script. This descriptive research uses pragmatic approach and theory. The collecting and analysing data are focused on the using of declarative, imperative, and interrogative sentences in the text of drama. The forms of those sentences will be analysed to find out the types of form of directive speech act, while the context of those sentences will be used to analyze the intended meaning of directive speech act uttered by speakers. The results of the research are found that, first, there are two types of the form of directive speech acts, direct directive speech acts and indirect directive speech acts. Direct directive speech acts are represented by imperative sentence without subject; imperative sentence with let; and negative imperative sentence. Meanwhile the indirect directive speech acts are represented by declarative sentence statement; declarative sentence if clause; negative declarative sentences; and interrogative sentences. Second, the intended meanings seen on drama script of Family 2.0 are command, prohibition, request, treat, and persuasion. It can be concluded that, the most frequent intended meaning appeared in directive speech acts on this script is command by the use of imperative forms. Then, the declarative and interrogative forms are used to request something by adults charaters; in contrast the kids characters use them to command and prohibit the hearer.<strong></strong></p><strong>Keywords: </strong> family 2.0, pragmatic, speech act, directive, form and intended meaning

Probability Logic and F

1976 ◽  
Vol 43 (2) ◽  
pp. 254-265
Author(s):  
A. I. Dale
Keyword(s):  
Probability Logic
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