Explanatory Nonmonotonic Reasoning

Bochman, Alexander

doi:10.1142/5707

Cited by 18 publications

(26 citation statements)

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“…12 As we will argue in Section 3, the 12 In [29] Makinson and van der Torre also present modal characterizations of some (unconstrained) I/O functions. However, their translation does not cover the four cases where (OR) is invalid.…”

Section: An Alternative Characterizationmentioning

confidence: 98%

“…All the sets of rules originally defined in [29] are normal (they consist of at least (SI), (AND) and (WO) which makes (EQ) derivable). The production inference relations in [12] validate additionally 6 Often the syntactic versions of I/O logics are written as deriv R while out R is reserved for the semantic versions. In this paper we will stick to out R for the syntactic versions due to its suggestive name: the function produces output.…”

Section: If (A C) and (B C) Then (A ∨ B C) (Or)mentioning

confidence: 99%

“…It belongs to a broader family of formal systems developed with this purpose in mind, such as, for instance, Gabbay [17], Crocco et al [16], Kraus et al [24], Lehmann et al [25], and Boutilier [14]. I/O logics also provided the groundworks for Bochman's production inference relations that are useful to model causal and abductive inferences [12]. As argued in [32], the main motivation for I/O logic concerns problems of deontic logic.…”

Section: Introductionmentioning

confidence: 99%

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Adaptive Logic Characterizations of Input/Output Logic

2016

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Abstract.We translate unconstrained and constrained input/output logics as introduced by Makinson and van der Torre to modal logics, using adaptive logics for the constrained case. The resulting reformulation has some additional benefits. First, we obtain a prooftheoretic (dynamic) characterization of input/output logics. Second, we demonstrate that our framework naturally gives rise to useful variants and allows to express important notions that go beyond the expressive means of input/output logics, such as violations and sanctions.

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Section: An Alternative Characterizationmentioning

confidence: 98%

Section: If (A C) and (B C) Then (A ∨ B C) (Or)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Adaptive Logic Characterizations of Input/Output Logic

2016

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“…For our reconstruction, the following questions can be asked (where the second could provide a kind of operational semantics analogous to the semantics of input/output logics [17], and the third to the semantics of input/output logic given in [4] The following theorem illustrates a simpler case.…”

Section: Etc Moreover Consider the Following Proof Rules: Conjunctimentioning

confidence: 99%

“…Makinson and van der Torre illustrate how to recapture input/output logic in modal logic, and thus give it a classical possible worlds semantics. More elegantly, as illustrated by Bochman [4], the operational semantics of input/output logic can be rephrased as a bimodel semantics, in which a model of a set of conditionals is a pair of partial models from the base logic (in this paper, propositional logic).…”

Section: Introductionmentioning

confidence: 99%

A Logical Architecture of a Normative System

Boella

Torre

2006

Deontic Logic and Artificial Normative Systems

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Abstract. Logical architectures combine several logics into a more complex logical system. In this paper we study a logical architecture using input/output operations corresponding to the functionality of logical components. We illustrate how the architectural approach can be used to develop a logic of a normative system based on logics of counts-as conditionals, institutional constraints, obligations and permissions. In this example we adapt for counts-as conditionals and institutional constraints a proposal of Jones and Sergot, and for obligations and permissions we adapt the input/output logic framework of Makinson and van der Torre. We use our architecture to study logical relations among counts-as conditionals, institutional constraints, obligations and permissions. We show that in our logical architecture the combined system of counts-as conditionals and institutional constraints reduces to the logic of institutional constraints, which again reduces to an expression in the underlying base logic. Counts-as conditionals and institutional constraints are defined as a pre-processing step for the regulative norms. Permissions are defined as exceptions to obligations and their interaction is characterized.

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Nonmonotonic Logics and Their Algebraic Foundations

Truszczyński

2006

Computer Science Logic

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Abstract. The goal of this note is to provide a background and references for the invited lecture presented at Computer Science Logic 2006. We briefly discuss motivations that led to the emergence of nonmonotonic logics and introduce two major nonmonotonic formalisms, default and autoepistemic logics. We then point out to algebraic principles behind the two logics and present an abstract algebraic theory that unifies them and provides an effective framework to study properties of nonmonotonic reasoning. We conclude with comments on other major research directions in nonmonotonic logics. Why nonmonotonic logicsIn the late 1970s, research on languages for knowledge representation, and considerations of basic patterns of commonsense reasoning brought attention to rules of inference that admit exceptions and are used only under the assumption of normality of the world in which one functions or to put it differently, when things are as expected.For instance, a knowledge base concerning a university should support an inference that, given no information that might indicate otherwise, if Dr. Jones is a professor at that university, then Dr. Jones teaches. Such conclusion might be sanctioned by an inference rule stating that normally university professors teach. In commonsense reasoning rules with exceptions are ubiquitous. Planning our day and knowing we are to have lunch with a friend, we might use the following rule: normally, lunches end by 1:00pm. If nothing we know indicates that the situation we are in is not normal, we use this rule and conclude that our lunch will be over by 1:00pm.The problem with such rules is that they do not lend themselves in any direct way to formalizations in terms of first-order logic, unless all exceptions are known and explicitly represented -an unrealistic expectation in practice. The reason is that standard logical inference is monotone: whenever a sentence α is a consequence of a set T of sentences then α is also a consequence of any set of sentences T ′ such that T ⊆ T ′ . On the other hand, it is clear that reasoning with normality rules when complete information is unavailable, is not monotone. In our lunch scenario, we may conclude that the lunch will be over by 1:00pm. However, if we learn that our friend will be delayed, the normality assumption is no longer valid our earlier inference is unsupported; we have to withdraw it.Such reasoning, where additional information may invalidate conclusions, is called nonmonotonic. As we briefly noted above, it is common. It has been a focus of extensive

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Explanatory Nonmonotonic Reasoning

Cited by 18 publications

References 0 publications

Adaptive Logic Characterizations of Input/Output Logic

Adaptive Logic Characterizations of Input/Output Logic

A Logical Architecture of a Normative System

Nonmonotonic Logics and Their Algebraic Foundations

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