Neil Tennant
- Published in print:
- 2012
- Published Online:
- September 2012
- ISBN:
- 9780199655755
- eISBN:
- 9780191742125
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199655755.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics, Metaphysics/Epistemology
This account of rational belief revision explains how a rational agent ought to proceed when adopting a new belief — a difficult matter if the new belief contradicts the agent’s old beliefs. Belief ...
More
This account of rational belief revision explains how a rational agent ought to proceed when adopting a new belief — a difficult matter if the new belief contradicts the agent’s old beliefs. Belief systems are modeled as finite dependency networks. So one can attend not only to what the agent believes, but also to the variety of reasons the agent has for so believing. The computational complexity of the revision problem is characterized. Algorithms for belief revision are formulated, and implemented in Prolog. The implementation tests well on a range of simple belief‐revision problems that pose a variety of challenges for any account of belief‐revision. The notion of ‘minimal mutilation’ of a belief system is explicated precisely. The proposed revision methods are invariant across different global justificatory structures (foundationalist, coherentist, etc.). They respect the intuition that, when revising one's beliefs, one should not hold on to any belief that has lost all its former justifications. The limitation to finite dependency networks is shown not to compromise theoretical generality. This account affords a novel way to argue that there is an inviolable core of logical principles. These principles, which form the system of Core Logic, cannot be given up, on pain of not being able to carry out the reasoning involved in rationally revising beliefs. The book ends by comparing and contrasting the new account with some major representatives of earlier alternative approaches, from the fields of formal epistemology, artificial intelligence and mathematical logic.Less
This account of rational belief revision explains how a rational agent ought to proceed when adopting a new belief — a difficult matter if the new belief contradicts the agent’s old beliefs. Belief systems are modeled as finite dependency networks. So one can attend not only to what the agent believes, but also to the variety of reasons the agent has for so believing. The computational complexity of the revision problem is characterized. Algorithms for belief revision are formulated, and implemented in Prolog. The implementation tests well on a range of simple belief‐revision problems that pose a variety of challenges for any account of belief‐revision. The notion of ‘minimal mutilation’ of a belief system is explicated precisely. The proposed revision methods are invariant across different global justificatory structures (foundationalist, coherentist, etc.). They respect the intuition that, when revising one's beliefs, one should not hold on to any belief that has lost all its former justifications. The limitation to finite dependency networks is shown not to compromise theoretical generality. This account affords a novel way to argue that there is an inviolable core of logical principles. These principles, which form the system of Core Logic, cannot be given up, on pain of not being able to carry out the reasoning involved in rationally revising beliefs. The book ends by comparing and contrasting the new account with some major representatives of earlier alternative approaches, from the fields of formal epistemology, artificial intelligence and mathematical logic.
Neil Tennant
- Published in print:
- 2012
- Published Online:
- September 2012
- ISBN:
- 9780199655755
- eISBN:
- 9780191742125
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199655755.003.0004
- Subject:
- Philosophy, Logic/Philosophy of Mathematics, Metaphysics/Epistemology
This is the heart of the formal theory. Mathematically rigorous definitions are provided of all the formal notions that have been gently introduced in the earlier discussion. The main data type of a ...
More
This is the heart of the formal theory. Mathematically rigorous definitions are provided of all the formal notions that have been gently introduced in the earlier discussion. The main data type of a step is defined, and the central concept of a dependency network is defined in terms of steps. The concept of a minimally mutilating contraction can then be explicated. Interest in the computational complexity of the contraction problem is motivated by thoroughly surveying known results about the (sometimes horrendous) complexities of various other decision problems of a logical nature. This is in order to provide a context within which the complexity results for contraction should strike the reader as both interesting and welcome. The contraction problem is rigorously characterized, including the hard version that involves the (now precisely explicated) desideratum of minimal mutilation. The simplest version of the contraction problem is shown to be NP-complete; the harder version, involving minimal mutilation, is shown to be at just the next level up in the so-called polynomial hierarchyLess
This is the heart of the formal theory. Mathematically rigorous definitions are provided of all the formal notions that have been gently introduced in the earlier discussion. The main data type of a step is defined, and the central concept of a dependency network is defined in terms of steps. The concept of a minimally mutilating contraction can then be explicated. Interest in the computational complexity of the contraction problem is motivated by thoroughly surveying known results about the (sometimes horrendous) complexities of various other decision problems of a logical nature. This is in order to provide a context within which the complexity results for contraction should strike the reader as both interesting and welcome. The contraction problem is rigorously characterized, including the hard version that involves the (now precisely explicated) desideratum of minimal mutilation. The simplest version of the contraction problem is shown to be NP-complete; the harder version, involving minimal mutilation, is shown to be at just the next level up in the so-called polynomial hierarchy
Neil Tennant
- Published in print:
- 2012
- Published Online:
- September 2012
- ISBN:
- 9780199655755
- eISBN:
- 9780191742125
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199655755.003.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics, Metaphysics/Epistemology
This chapter distinguishes logic as a theory of belief‐statics from our sought account of belief dynamics. The various kinds of belief change are classified. These are: surrendering, adopting or ...
More
This chapter distinguishes logic as a theory of belief‐statics from our sought account of belief dynamics. The various kinds of belief change are classified. These are: surrendering, adopting or switching individual beliefs; and thereby contracting, expanding or revising one’s system of beliefs. Our account of the epistemic norms involved is agent-centric. The idealized figure of the logical paragon (as opposed to the completely fictional figure of the ‘logical saint’) is introduced as the guiding model of a rational agent who is thoroughly competent in matters of belief change. The chapter discusses what a theory of belief change needs to characterize or make feasible. Two key constraints are formulated: both minimal mutilation and minimal bloating of systems of belief undergoing contractions and revisions needs to be explicated (and ensured). The explicit goal is to provide a computationally implementable account of belief change. The chapter foreshadows welcome results to be proved about the computational complexity of the contraction problem. It stresses that our account of belief dynamics will be able to cope with differences among different schools, or ‘‐isms’, in epistemology, regarding permissible global patterns of support or justification among beliefs. The chapter includes an important discussion of methodology, invoking the contrast between propositional and first-order logic as a case study, in order to highlight the virtues of simplicity in formal modeling. This chapter promises to be an account of belief change under judiciously chosen simplifying assumptions that nevertheless allow a rich structure to come into focus, and challenging problems to emerge.Less
This chapter distinguishes logic as a theory of belief‐statics from our sought account of belief dynamics. The various kinds of belief change are classified. These are: surrendering, adopting or switching individual beliefs; and thereby contracting, expanding or revising one’s system of beliefs. Our account of the epistemic norms involved is agent-centric. The idealized figure of the logical paragon (as opposed to the completely fictional figure of the ‘logical saint’) is introduced as the guiding model of a rational agent who is thoroughly competent in matters of belief change. The chapter discusses what a theory of belief change needs to characterize or make feasible. Two key constraints are formulated: both minimal mutilation and minimal bloating of systems of belief undergoing contractions and revisions needs to be explicated (and ensured). The explicit goal is to provide a computationally implementable account of belief change. The chapter foreshadows welcome results to be proved about the computational complexity of the contraction problem. It stresses that our account of belief dynamics will be able to cope with differences among different schools, or ‘‐isms’, in epistemology, regarding permissible global patterns of support or justification among beliefs. The chapter includes an important discussion of methodology, invoking the contrast between propositional and first-order logic as a case study, in order to highlight the virtues of simplicity in formal modeling. This chapter promises to be an account of belief change under judiciously chosen simplifying assumptions that nevertheless allow a rich structure to come into focus, and challenging problems to emerge.
