Hintikka, J.: Impossible Possible Worlds Vindicated. Journal of Philosophical Logic 4 (1975) 475--484  Home/Search   Document Not in Database   Summary   Related Articles   Check

....property since the equivalence relation (consequence relation) on classical propositional formulas is decidable. 3 Related Work In this section, we briefly survey previous approaches to the problem of logical omniscience and point out similarities and di#erences with our approach. Hintikka [4, 5] and Rantala [7] saw the problem of logical omniscience mostly as a result of unrealistic principles in a formal model of knowledge. The solution they favoured was to make the principles invalid by changing the possible worlds semantics so that logically equivalent formulas do not necessarily ....

Hintikka, J.: Impossible possible worlds vindicated. Journal of Philosophical Logic, 4:475--484, 1975.

....knowledge and beliefs. Whether there exist other kinds of implication which are intuitive and avoid logical omniscience remains an interesting problem. In this paper, first of all, we reexamine the problem of logical omniscience, and discuss proposed strategies to handle with the problem. In [10], Hintikka asserts that the only reasonable way of solving th problem of logical omniscience is to countenance worlds that are epistemically possible but not logically possible. However, in [7] Fagin and Halpern present some awareness logics, and claim that in the logics agents are not logically ....

....# L(i) # L(i) Fagin and Halpern claim that their general awareness logic has the property that agents are not logically omniscient, and the logic is more suitable than traditional logics for modelling beliefs of humans (or machines) with limited reasoning capabilities. However, in [10], Hintikka asserts that the only reasonable way of solving the problem of logical omniscience is to countenance worlds that are epistemically possible but not logically possible. Now, a contradiction is avoided, thanks to the distinction between actual belief Here the notations are di#erent from ....

Hintikka, J., Impossible possible worlds vindicated. J. Philosophy 4(1975), 475-484.

....not be interpreted as: the use of Godel numbers in the semantics seems unavoidable we use Godel numbers to encode our stratified semantics in higher order logic, but even without that, the stratified semantics itself contains syntactic types (in the allocset i ) Game semantics. Hintikka [11] advocated the use of game theoretical semantics to model possible worlds. Game semantics is especially useful in removing from consideration all impossible possible worlds. Abramsky, Honda and McCusker[1] describe a game semantics of general references that they show to be fully abstract. In ....

K. J. Hintikka. Impossible possible worlds vindicated. Journal of Philosophical Logic, 4:475--484, 1975.

.... standard way of providing a meaning to the modal formulas of these logics is to use the possible worlds model ( 2] and its associated Kripke semantics ( 3] This semantics is quite natural and intuitive, but it is well known that the agents modelled in this framework are logically omniscient ([4]) Therefore, this semantics is unsuitable to model the beliefs of realistic, non ideal agents. The aim of our work is to provide a plausible way of modelling the beliefs of non logically omniscient agents, while keeping the essence and the beauty of the possible worlds model and the Kripke ....

J. Hintikka, Impossible possible worlds vindicated, J. of Phil. Logic 4 (1975), 475-484.

....basic idea underlying Kripke semantics is that besides the true state of the world, there are a number of other possible states of the world. An agent is said to believe OE if OE is true in all the worlds he think possible. As has been frequently pointed out in the literature (see, for instance, [14]) Kripke semantics assumes an ideal rational agent, with infinite computational power and which suffers from the problem of what Hintikka calls logical onmiscence. Logical onmiscence means that agents are assumed to be so clever that (i) they must know all the valid formulae, and that (ii) ....

J. Hintikka. Impossible possible worlds vindicated. Journal of Philosophical Logic, 4:475--484, 1975.

....Modelling tools 2. 1 Conceivable situations We have just mentioned several proposals that have tried to solve (or, at least, partially alleviate) the problems of logical omniscience and perfect reasoning (both in AI and in Philosophy) A particularly interesting suggestion was made by Hintikka in [Hint75], where he proposed the idea of considering [logically] impossible [epistemically] possible worlds 11 ; he seems not to have pursued this idea, though. This is the path followed in our work, as will be apparent in the rest of this document. The main roots of these problems are the assumptions ....

....a base set of beliefs and a (possibly incomplete) set of inference rules (see [More97] A similar idea is followed by Benerecetti et al. in [Bene97] where the notion of a context (an axiomatic formal system) is used to model the reasoning capabilities of ideal and real reasoners. 11 Hintikka ([Hint75]) defines them as those worlds so subtly inconsistent that the inconsistency could not be expected to be perceived by an everyday logician, however competent. He then identifies this kind of worlds with those urn models ( Rant75] which vary so subtly as to be indistinguishable from invariant ones ....

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Hintikka, J., "Impossible possible worlds vindicated", Journal of Philosophical Logic 4, pp. 475-484, 1975.

.... standard way of providing a meaning to the modal formulas of these logics is to use the possible worlds model ( 2] and its associated Kripke semantics ( 3] This semantics is quite natural and intuitive, but it is well known that the agents modelled in this framework are logically omniscient ([4]) because they must believe all valid formulas and all the logical consequences of their beliefs. Therefore, this semantics is unsuitable to model the beliefs of realistic, non ideal agents. The aim of our work is to provide a plausible way of modelling the beliefs of non logically omniscient ....

J. Hintikka, Impossible possible worlds vindicated, Journal of Philosophical Logic 4 (1975), 475-484.

....p. 319) This definition of knowledge leads to what Hacking calls personal possibility, and to his preferred, sentential form of personal probability. This solves Savage s problem in one 1. Logical closure on beliefs is referred to as logical omniscience in the logic community (such as [Hintikka 75]) according to Konolige [Konolige 86] p q 109 sense, by making the theory weaker. Now that agents do not make all logical deductions, to restore some of the power of decision theory we would need to model what deductions they do make. But Hacking realized this still left a question ....

Jakko Hintikka. Impossible possible worlds vindicated. Journal of Philosophical Logic, 4:475-484, 1975.

.... reasoner) In the AI literature most authors deal with these problems by introducing impossible possible worlds, e.g. possible worlds where logical connectives do not behave in the usual way, or tautologies may not be true, or inconsistent formulas may hold (see e.g. impossible possible worlds in [HINT75], non classical worlds in [CRES72] non standard worlds in [RESC79] or situations in [LEVE84] These semantic approaches somehow alleviate the problems of logical omniscience and perfect reasoning, but they cause different problems (see e.g. McAR88] REIC89] for detailed reviews of these and ....

Hintikka, J., `Impossible possible worlds vindicated', Journal of Philosophical Logic 4, 475-484, 1975.

....to agent 3 (the blue army) standard epistemic logic allows us to infer that agent 3 knows A s , is therefore able to decrypt the messages and hence knows A a . Weaker logics do not help to explain why he does not know the attack plan, either. The socalled impossible worlds approach ([9], 12] cannot offer any acceptable explanation: it is very odd to explain the fact that the blue army do not know the secret key by saying that some axioms of logic or of number theory are false in some impossible possible worlds. As it is plausible to assume that classical logic is used in the ....

J. Hintikka. Impossible possible worlds vindicated. Journal of Philosophical Logic, pages 475--484, 1975.

....networks in terms of an agent. The agent has beliefs and performs actions (see [9] Such an agent is (a model of) a cognitive agent [17] Among the actions the agent can perform is the new believing of a previously not believed proposition. Rather than having the agent be logically omniscient [3] (i.e. believe all the logical consequents of its beliefs) at any time, the agent will believe only those logical consequents of its beliefs that it has come to believe by consciously performing the act of believing them, or those it has come to believe by thinking of them after already ....

J. Hintikka. Impossible possible worlds vindicated. Journal of Philosophical Logic, 4:475--484, 1975.

....efficiently (assuming is in conjunctive normal form) Yet another approach has been called the impossible worlds approach. The idea here is that the possible worlds, where all the customary rules of classical logic hold, are augmented by impossible worlds, where they do not [Cresswell 1973; Hintikka 1975; Rantala 1982; Rescher and Brandom 1979; Wansing 1990] For example, in an impossible world, it may be the case that p :p holds, while this cannot be the case in a possible world. It is still the case that an agent knows if is true in all the worlds that he considers possible, but now an ....

Hintikka, J. (1975). Impossible possible worlds vindicated. Journal of Philosophical Logic 4, 475--484.

....logic. One denies the universal validity of the mentioned inference rules NEC, MON, and CGR, or one of the essential axioms like K. In fact, almost all attempts to solve the LOP have in common that they consider systems that are weaker than the standard modal epistemic logics (cf. 3] 5] 6] [14], 18] 21] 22] 23] 25] One can construct systems that falsify either the inference rules or the axioms of the standard modal systems. For example, modal systems which are not normal can be used to describe an agent who does not know all logical truths. If we use neighborhood semantics ....

J. Hintikka. Impossible possible worlds vindicated. Journal of Philosophical Logic, 4:475--484, 1975.

....reasoning. Several proposals that have tried to solve (or, at least, partially alleviate) them have been put forward in the AI and the philosophical literature (e.g. McAR88] REIC89] or [FAGI95] contain detailed reviews of the most relevant approaches) Hintikka made an interesting suggestion in [HINT75], where he proposed the idea of considering [logically] impossible [epistemically] possible worlds, but later he seems not to have pursued this idea. This is the path followed in this work, as will be apparent in the rest of this report. The main roots of these problems, as has been stated above, ....

.... In fact, many people have proposed to consider impossible possible worlds, in the sense of having possible worlds where the usual logical connectives do not behave in the usual way, or tautologies may not be true, or inconsistent formulas may hold (see e.g. impossible possible worlds in [HINT75], non classical worlds in [CRES72] non standard worlds in [RESC79] or situations in [LEVE84] The drawback of these approaches is that, although they alleviate the problems of logical omniscience and perfect reasoning, they cause different problems. Basically, the main inconvenient of the ....

Hintikka, J., "Impossible possible worlds vindicated", Journal of Philosophical Logic 4, pp. 475-484, 1975.

....have been interested in MV logics for several reasons. Starting from the work on relevance logics, Frisch introduced in [12, 13] a notion of weak inference for capturing the idea of local reasoning. In the field of epistemic reasoning, the impossible world approach defined by Hintikka in [16] i.e. each world is a multivalued truth assignment is a common technique for dealing with the logical omniscience problem. An example of such an approach is reported by Fagin, Halpern and Vardi in [10] MV logics have also been used as a uniform framework for representing sophisticated ....

J. Hintikka. Impossible possible worlds vindicated. Journal of Philosophical Logic, 4:475--484, 1975.

....which goes back to Hintikka [Hin62] is in terms of possible worlds. In this approach, an agent is said to know a fact if is true in all the worlds he considers possible. As has been frequently pointed out, this approach suffers from what Hintikka termed the logical omniscience problem [Hin75]: agents are so intelligent that they know all the logical consequences of their knowledge. Thus, if an agent knows all of the formulas in a set Sigma and if Sigma logically implies the formula , then the agent also knows . In particular, they know all valid formulas (including all tautologies ....

J. Hintikka. Impossible possible worlds vindicated. Journal of Philosophical Logic, 4:475--484, 1975.

.... (que tienen una limitaci on de recursos que les imposibilita ser razonadores perfectos) Ha habido muchas aproximaciones que han intentado solucionar o mitigar parcialmente estos problemas, ya sea de forma sint actica ( VARD86] KONO86] HINT86] o sem antica ( MONT70] CRES72] RANT75] [HINT75], RESC79] LEVE84] FAGI85] LAKE94] DELG95] Sin embargo, ninguna de estas aproximaciones parece solucionarlos plenamente. El objetivo de este trabajo es analizar la ra iz de estos problemas y proponer una nueva aproximaci on desde una nueva perspectiva. En este art iculo, se muestra c omo ....

.... que han propuesto mundos posibles imposibles, en el sentido de tener mundos posibles en los que las conectivas l ogicas no se comportan de la manera est andar, o las tautolog ias pueden no ser ciertas, o f ormulas inconsistentes pueden ser ciertas (ver e.g. mundos posibles imposibles en [HINT75], mundos no cl asicos en [CRES72] mundos no est andar en [RESC79] o situaciones en [LEVE84] Con la definici on sint actica de mundos posibles considerada se evitan los problemas de la omnisciencia l ogica y el razonamiento perfecto, pero la contrapartida es la debilidad de esta aproximaci on, ....

Hintikka, J., "Impossible possible worlds vindicated", Journal of Philosophical Logic 4, pp. 475-484, 1975.

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Hintikka, J.: Impossible Possible Worlds Vindicated. Journal of Philosophical Logic 4 (1975) 475--484

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J. Hintikka. Impossible possible worlds vindicated. Journal of Philisophical Logic, 4:475--484, 1675.

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J. Hintikka. Impossible possible worlds vindicated. Journal of Philisophical Logic, 4:475--484, 1675. 17

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J. Hintikka. Impossible possible worlds vindicated. Journal of Philisophical Logic, 4:475--484, 1675.

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Jaakko Hintikka. Impossible possible worlds vindicated. Journal of Philosophical Logic, 4:475-- 484, 1975.

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Hintikka, J., 1975. Impossible possible worlds vindicated, Jour- nal o) e Philosophical Logic 4, 367-379.

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Hintikka, J.: 1975, Impossible Possible Worlds Vindicated, Journal of

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J. Hintikka. Impossible possible worlds vindicated. Journal of Philosophical Logic, Vol.44, 1975.

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