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Semantical considerations on FloydHoare Logic
, 1976
"... This paper deals with logics of programs. The objective is to formalize a notion of program description, and to give both plausible (semantic) and effective (syntactic) criteria for the notion of truth of a description. A novel feature of this treatment is the development of the mathematics underlyi ..."
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Cited by 210 (10 self)
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This paper deals with logics of programs. The objective is to formalize a notion of program description, and to give both plausible (semantic) and effective (syntactic) criteria for the notion of truth of a description. A novel feature of this treatment is the development of the mathematics underlying FloydHoare axiom systems independently of such systems. Other directions that such research might take are considered.
MEBN: A Language for FirstOrder Bayesian Knowledge Bases
"... Although classical firstorder logic is the de facto standard logical foundation for artificial intelligence, the lack of a builtin, semantically grounded capability for reasoning under uncertainty renders it inadequate for many important classes of problems. Probability is the bestunderstood and m ..."
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Cited by 45 (18 self)
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Although classical firstorder logic is the de facto standard logical foundation for artificial intelligence, the lack of a builtin, semantically grounded capability for reasoning under uncertainty renders it inadequate for many important classes of problems. Probability is the bestunderstood and most widely applied formalism for computational scientific reasoning under uncertainty. Increasingly expressive languages are emerging for which the fundamental logical basis is probability. This paper presents MultiEntity Bayesian Networks (MEBN), a firstorder language for specifying probabilistic knowledge bases as parameterized fragments of Bayesian networks. MEBN fragments (MFrags) can be instantiated and combined to form arbitrarily complex graphical probability models. An MFrag represents probabilistic relationships among a conceptually meaningful group of uncertain hypotheses. Thus, MEBN facilitates representation of knowledge at a natural level of granularity. The semantics of MEBN assigns a probability distribution over interpretations of an associated classical firstorder theory on a finite or countably infinite domain. Bayesian inference provides both a proof theory for combining prior knowledge with observations, and a learning theory for refining a representation as evidence accrues. A proof is given that MEBN can represent a probability distribution on interpretations of any finitely axiomatizable firstorder theory.
A Taxonomy of Csystems
, 2002
"... The logics of formal inconsistency (LFIs) are paraconsistent logics which permit us to internalize the concepts of consistency or inconsistency inside our object language, introducing new operators to talk about them, and allowing us, in principle, to logically separate the notions of contradictorin ..."
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Cited by 41 (15 self)
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The logics of formal inconsistency (LFIs) are paraconsistent logics which permit us to internalize the concepts of consistency or inconsistency inside our object language, introducing new operators to talk about them, and allowing us, in principle, to logically separate the notions of contradictoriness and of inconsistency. We present the formal definitions of these logics in the context of General Abstract Logics, argue that they in fact represent the majority of all paraconsistent logics existing up to this point, if not the most exceptional ones, and we single out a subclass of them called Csystems, as the LFIs that are built over the positive basis of some given consistent logic. Given precise characterizations of some received logical principles, we point out that the gist of paraconsistent logic lies in the Principle of Explosion, rather than in the Principle of NonContradiction, and we also sharply distinguish these two from the Principle of NonTriviality, considering the next various weaker formulations of explosion, and investigating their interrelations. Subsequently, we present the syntactical formulations of some of the main Csystems based on classical logic, showing how several wellknown logics in the literature can be recast as such a kind of Csystems, and carefully study their properties and shortcomings, showing for instance how they can be used to faithfully
Toward the use of an upper ontology for U.S. government and U.S. military domains: An evaluation
 Submission to Workshop on Information Integration on the Web (IIWeb04), in conjunction with VLDB2004
, 2004
"... Sponsor: ESC Contract No.: FA9721040001 ..."
FirstOrder Bayesian Logic
, 2005
"... Uncertainty is a fundamental and irreducible aspect of our knowledge about the world. Until recently, classical firstorder logic has reigned as the de facto standard logical foundation for artificial intelligence. The lack of a builtin, semantically grounded capability for reasoning under uncertai ..."
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Cited by 8 (3 self)
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Uncertainty is a fundamental and irreducible aspect of our knowledge about the world. Until recently, classical firstorder logic has reigned as the de facto standard logical foundation for artificial intelligence. The lack of a builtin, semantically grounded capability for reasoning under uncertainty renders classical firstorder logic inadequate for many important classes of problems. Generalpurpose languages are beginning to emerge for which the fundamental logical basis is probability. Increasingly expressive probabilistic languages demand a theoretical foundation that fully integrates classical firstorder logic and probability. In firstorder Bayesian logic (FOBL), probability distributions are defined over interpretations of classical firstorder axiom systems. Predicates and functions of a classical firstorder theory correspond to a random variables in the corresponding firstorder Bayesian theory. This is a natural correspondence, given that random variables are formalized in mathematical statistics as measurable functions on a probability space. A formal system called MultiEntity Bayesian Networks (MEBN) is presented for composing distributions on interpretations by instantiating and combining parameterized fragments of directed graphical models. A construction is given of a MEBN theory that assigns a nonzero
Towards a radical constructivist understanding of science
 Foundations of Science
"... Abstract. Constructivism is the idea that we construct our own world rather than it being determined by an outside reality. Its most consistent form, Radical Constructivism (RC), claims that we cannot transcend our experiences. Thus it doesn’t make sense to say that our constructions gradually appro ..."
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Abstract. Constructivism is the idea that we construct our own world rather than it being determined by an outside reality. Its most consistent form, Radical Constructivism (RC), claims that we cannot transcend our experiences. Thus it doesn’t make sense to say that our constructions gradually approach the structure of an external reality. The mind is necessarily an epistemological solipsist, in contrast to being an ontological solipsist who maintains that this is all there is, namely a single mind within which the only world exists. RC recognizes the impossibility of the claim that the world does not exist. Yet, RC has the potential to go much further. I claim that RC provides the foundation of a new worldview in which we can overcome hard scientific problems. Thus, the paper is urging us to carry RC further, not just on philosophical grounds, but also into the domain of science.
forthcoming. “Epistemic Modals are AssessmentSensitive
 Who’s Afraid of Impossible Worlds?” Notre Dame Journal of Formal Logic
, 1997
"... By “epistemic modals, ” I mean epistemic uses of modal words: adverbs like “necessarily, ” “possibly, ” and “probably, ” adjectives like “necessary,” “possible, ” and “probable, ” and auxiliaries like “might, ” “may, ” “must, ” and “could. ” It is hard to say exactly what makes a word modal, or what ..."
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Cited by 6 (0 self)
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By “epistemic modals, ” I mean epistemic uses of modal words: adverbs like “necessarily, ” “possibly, ” and “probably, ” adjectives like “necessary,” “possible, ” and “probable, ” and auxiliaries like “might, ” “may, ” “must, ” and “could. ” It is hard to say exactly what makes a word modal, or what makes
TruthMakers
, 1984
"... This paper is about such a theory. If we are right that the Tarskian account neglects precisely the atomic sentences, then its indeterminacy is not surprising ..."
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Cited by 5 (1 self)
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This paper is about such a theory. If we are right that the Tarskian account neglects precisely the atomic sentences, then its indeterminacy is not surprising
on Truth and Its Definition, in
 Logica ’96 – Proceedings of 10 th International Symposium (Filosofia
, 1997
"... Of his numerous investigations... Tarski was most proud of two: his work on truth and his design of an algorithm in 1930 to decide the truth or falsity of any sentence of the elementary theory of the high school Euclidean geometry. [...] His mathematical treatment of the semantics of languages and t ..."
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Cited by 2 (0 self)
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Of his numerous investigations... Tarski was most proud of two: his work on truth and his design of an algorithm in 1930 to decide the truth or falsity of any sentence of the elementary theory of the high school Euclidean geometry. [...] His mathematical treatment of the semantics of languages and the concept of truth has had revolutionary consequences for mathematics, linguistics, and philosophy, and Tarski is widely thought of as the man who "defined truth". The seeming simplicity of his famous example that the sentence "Snow is white " is true just in case snow is white belies the depth and complexity of the consequences which can be drawn from the possibility of giving a general treatment of the concept of truth in formal mathematical languages in a rigorous mathematical way. (J.W. Addison) As Anil Gupta observes, ‘there is much misunderstanding about Tarski’s work on truth’. 1 Here I want to examine four questions over which there has been considerable misunderstanding: (1) What is the semantic conception of truth? (2) What is the significance of translation in the criterion of material adequacy? (3) What is the status of Tsentences? (4) What role does the definition of truth by satisfaction play in Tarski’s thinking about truth?